Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We hereby consent to the incorporation by reference in the Registration Statement on Form S-3 (No. 333-209437) of PowerShares DB Precious Metals Fund (a series of PowerShares DB Multi-Sector Commodity Trust) of our report dated February 27, 2017 relating to the financial statements and the effectiveness of internal control over financial reporting, which appears in this Form 10-K.

/s/ PricewaterhouseCoopers LLP

Chicago, Illinois

February 27, 2017