<?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>109 - Disclosure - Investments in Mineral Properties</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>cx_01_January_2013_TO_30_June_2013</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001040482</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>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>4</Level><ElementName>us-gaap_MineralIndustriesDisclosuresTextBlock</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="cx_01_January_2013_TO_30_June_2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;table border="0" cellpadding="0" cellspacing="0" style="border-color: black; font-size: 10pt; border-collapse: collapse; font-family: times new roman,times,serif;" width="100%"&gt;
      &lt;tr&gt;
        &lt;td valign="top" width="5%"&gt;
          &lt;b&gt;4.&lt;/b&gt;
        &lt;/td&gt;
        &lt;td&gt;
          &lt;p align="justify" style="font-family: times new roman,times,serif; font-size: 10pt; margin: inherit;"&gt;
            &lt;b&gt;Investments in Mineral Properties&lt;/b&gt;
          &lt;/p&gt;
        &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
        &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
        &lt;td&gt;
          &lt;p align="justify" style="font-family: times new roman,times,serif; font-size: 10pt; margin: inherit;"&gt;
            During the six months ended June 30, 2013, the Company invested $43,180
            in one investment of mineral properties. During the year ended December 31, 2012, the Company invested a total of $355,242
            in four mineral properties and exchanged a Poston Prospect well with a book value of $41,000
            plus cash in the amount of $6,500
            for partial payment on a well located in the Oklahoma prospect. Management reviewed the carrying amount of the Company&amp;#8217;s investments in its oil and gas properties as of the balance sheet date and recognized an impairment expense in the amount of $0
            and $256,737
            for the six months ended June 30, 2013 and 2012, respectively. As of June 30, 2013 and December 31, 2012, the estimated fair value of mineral properties totaled $1,590,328
            and $1,582,324, net of accumulated amortization of $167,675
            and $132,499, respectively. As of June 30, 2013, the Company has total capitalized costs of mineral properties (gross) of $1,758,003
            ; $1,103,205
            in proved properties and $654,798
            in unproved properties. As of December 31, 2012, the Company has total capitalized costs of mineral properties (gross) of $1,714,822
            ; $1,103,205
            in proved properties and $611,617
            in unproved properties. Capitalized costs of proved properties are amortized using the straight-line method over the estimated useful life of each well. Unproved properties are excluded from amortization. Amortization expense for the six months ended June 30, 2013 and 2012 was $35,176
            and $60,808, respectively. A summary of investments follows:
          &lt;/p&gt;
        &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
        &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
        &lt;td&gt;&amp;#160;&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
        &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
        &lt;td&gt;
          &lt;p align="justify" style="font-family: times new roman,times,serif; font-size: 10pt; margin: inherit;"&gt;
            &lt;b&gt;S&amp;amp;W Oil &amp;amp; Gas, LLC - Poston Prospect&lt;/b&gt;
          &lt;/p&gt;
        &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
        &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
        &lt;td&gt;
          &lt;p align="justify" style="font-family: times new roman,times,serif; font-size: 10pt; margin: inherit;"&gt;
            On May 4, 2009, the Company entered into an Agreement with S&amp;amp;W Oil &amp;amp; Gas, LLC (&amp;#8220;S&amp;amp;W&amp;#8221;) to participate in the drilling for oil in the Poston Prospect #1 Lutters in Southwest Trego County, Kansas (the &amp;#8220;Poston Prospect&amp;#8221;). Pursuant to the agreement, the Company paid $64,500
            in exchange for a
            25% working interest in the
            81.5% net revenue interest in the Poston Prospect. Subsequent to acquiring the working interest, the Company paid $138,615
            in capitalized development costs necessary for completion of the initial well and the drilling and completion of a second well in the Poston Prospect. In 2011, the Company recognized an impairment of the investment in the amount of $93,879. During the year ended December 31, 2012, the Company sold its interest in the Poston Prospect for cash in the amount of $69,500, resulting in a gain of $2,621. This well contributed approximately
            5% of the Company&amp;#8217;s 2012 revenue and
            0% of the revenue for the six months ended June 30, 2013.
          &lt;/p&gt;
        &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
        &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
        &lt;td&gt;&amp;#160;&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
        &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
        &lt;td&gt;
          &lt;p align="justify" style="font-family: times new roman,times,serif; font-size: 10pt; margin: inherit;"&gt;
            &lt;b&gt;Oklahoma prospects&lt;/b&gt;
          &lt;/p&gt;
        &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
        &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
        &lt;td&gt;
          &lt;p align="justify" style="font-family: times new roman,times,serif; font-size: 10pt; margin: inherit;"&gt;
            During 2010 and 2011, the Company acquired various working interest percentages ranging from
            5% to
            50%, from Bay Petroleum for mineral properties located in Oklahoma in exchange for cash totaling $1,992,330. During the year ended December 31, 2011, one well was determined to be a &amp;#8220;dry hole&amp;#8221; and its full $80,000
            carrying value was impaired. During the year ended December 31, 2012, the Company acquired additional working interests in the Oklahoma prospects for cash in the amount of $355,242
            and property valued at $41,000. During the year ended December 31, 2012, two of the wells were determined to be uneconomic and $565,737
            of impairment was taken to reduce the properties to their fair value. The Oklahoma prospects wells contributed approximately
            95% of the Company&amp;#8217;s 2012 revenue and
            100% of the revenue for the six months ended June 30, 2013.
          &lt;/p&gt;
        &lt;/td&gt;
      &lt;/tr&gt;
    &lt;/table&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 mineral industries.</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Investments in Mineral Properties [Text Block]</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Investments in Mineral Properties</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.americanpetrohunter.com/taxonomy/role/NotesToFinancialStatementsMineralIndustriesDisclosuresTextBlock</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>1</NumberOfRows></InstanceReport>
