<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>1050 - Disclosure - Fair Value Measurement of Financial Instruments</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>D2013Q2YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001308711</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_FairValueDisclosuresAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Fair Value Measurement of Financial Instruments</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_FairValueDisclosuresTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-size:10.0pt;font-family:Times New Roman;"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;b&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt; FONT-WEIGHT: bold;" size="2"&gt;5.&lt;/font&gt;&lt;/b&gt;&lt;b&gt;&lt;font style="FONT-SIZE: 3pt; FONT-WEIGHT: bold;" size="1"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&lt;/font&gt;&lt;/b&gt; &lt;b&gt;&lt;font style="FONT-SIZE: 10pt; FONT-WEIGHT: bold;" size="2"&gt;Fair Value Measurement of Financial Instruments&lt;/font&gt;&lt;/b&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;We determined the following disclosure of estimated fair values using available market information and appropriate valuation methodologies.&amp;#160; Considerable judgment is necessary to interpret market data and develop the related estimates of fair value.&amp;#160; Accordingly, the estimates presented are not necessarily indicative of the amounts that could be realized upon disposition of the financial instruments.&amp;#160; The use of different market assumptions and/or estimation methodologies may have a material effect on the estimated fair value amounts.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-ALIGN: center; MARGIN: 0in 0in 0pt;" align="center"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;As of June&amp;#160;30, 2013 and December&amp;#160;31, 2012, management estimated that the carrying value of cash and cash equivalents, restricted cash, accounts receivable, accounts payable, accrued expenses, other liabilities, payables/receivables from related parties, and distributions payable were at amounts that reasonably approximated their fair value based on their highly liquid nature and/or short-term maturities, and the carrying value of notes receivable reasonably approximated fair value based on expected interest rates for notes to similar borrowers with similar terms and remaining maturities.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;The notes payable totaling $140.5 million and $164.2 million including the loan secured by Becket House (classified as held for sale) as of June&amp;#160;30, 2013 and December&amp;#160;31, 2012, respectively, have a fair value of approximately $140.2&amp;#160;million and $163.8&amp;#160;million, respectively, based upon interest rates for mortgages with similar terms and remaining maturities that management believes we could obtain.&amp;#160; Interest rate swaps and caps are recorded at their respective fair values in prepaid expenses and other assets.&amp;#160; The fair value of the notes payable is categorized as a Level 2 basis.&amp;#160;&amp;#160;The fair value is estimated using a discounted cash flow analysis valuation on the borrowing rates currently available for loans with similar terms and maturities.&amp;#160;&amp;#160;The fair value of the notes payable was determined by discounting the future contractual interest and principal payments by a market rate.&lt;/font&gt;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.5in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;The fair value estimates presented herein are based on information available to our management as of June&amp;#160;30, 2013 and December&amp;#160;31, 2012.&amp;#160; Although our management is not aware of any factors that would significantly affect the estimated fair value amounts, such amounts have not been comprehensively revalued for purposes of these condensed consolidated financial statements since those respective dates, and current estimates of fair value may differ significantly from the amounts presented.&lt;/font&gt;&lt;/p&gt;
&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for the fair value of financial instruments (as defined), including financial assets and financial liabilities (collectively, as defined), and the measurements of those instruments as well as disclosures related to the fair value of non-financial assets and liabilities. Such disclosures about the financial instruments, assets, and liabilities would include: (1) the fair value of the required items together with their carrying amounts (as appropriate); (2) for items for which it is not practicable to estimate fair value, disclosure would include: (a) information pertinent to estimating fair value (including, carrying amount, effective interest rate, and maturity, and (b) the reasons why it is not practicable to estimate fair value; (3) significant concentrations of credit risk including: (a) information about the activity, region, or economic characteristics identifying a concentration, (b) the maximum amount of loss the entity is exposed to based on the gross fair value of the related item, (c) policy for requiring collateral or other security and information as to accessing such collateral or security, and (d) the nature and brief description of such collateral or security; (4) quantitative information about market risks and how such risks are managed; (5) for items measured on both a recurring and nonrecurring basis information regarding the inputs used to develop the fair value measurement; and (6) for items presented in the financial statement for which fair value measurement is elected: (a) information necessary to understand the reasons for the election, (b) discussion of the effect of fair value changes on earnings, (c) a description of [similar groups] items for which the election is made and the relation thereof to the balance sheet, the aggregate carrying value of items included in the balance sheet that are not eligible for the election; (7) all other required (as defined) and desired information.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 107

 -Paragraph 15A

 -Subparagraph a-d

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 107

 -Paragraph 15C, 15D

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 107

 -Paragraph 3, 10, 14, 15

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 157

 -Paragraph 32, 33, 34

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 825

 -SubTopic 10

 -Section 50

 -Paragraph 21

 -URI http://asc.fasb.org/extlink&amp;oid=7491637&amp;loc=d3e13537-108611



Reference 6: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 133

 -Paragraph 44A, 44B

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 7: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 825

 -SubTopic 10

 -Section 50

 -Paragraph 10

 -URI http://asc.fasb.org/extlink&amp;oid=7491637&amp;loc=d3e13433-108611



Reference 8: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 825

 -SubTopic 10

 -Section 50

 -Paragraph 28

 -URI http://asc.fasb.org/extlink&amp;oid=6957238&amp;loc=d3e14064-108612



Reference 9: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 820

 -SubTopic 10

 -Section 50

 -Paragraph 2

 -URI http://asc.fasb.org/extlink&amp;oid=7578670&amp;loc=d3e19207-110258



Reference 10: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 825

 -SubTopic 10

 -Section 50

 -Paragraph 30

 -URI http://asc.fasb.org/extlink&amp;oid=6957238&amp;loc=d3e14172-108612



Reference 11: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 825

 -SubTopic 10

 -Section 50

 -Paragraph 16

 -URI http://asc.fasb.org/extlink&amp;oid=7491637&amp;loc=d3e13504-108611



Reference 12: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 107

 -Paragraph 15B

 -Subparagraph a, b

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 13: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 159

 -Paragraph 17-22, 27, 28

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Fair Value Measurement of Financial Instruments</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Fair Value Measurement of Financial Instruments</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.behringerharvard.com/role/DisclosureFairValueMeasurementOfFinancialInstruments</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
