Exhibit 32.1

Certifications

Pursuant
to Section 906 of the Sarbanes-Oxley Act of 2002

(Subsections (a) and (b) of Section 1350, Chapter 63 of
Title 18, United States Code)

In connection with the Annual Report of Orexigen Therapeutics, Inc., a Delaware corporation (the
Company), on Form 10-K/A for the period ended December 31, 2015, as filed with the Securities and Exchange Commission on the date hereof (the Report), I, Michael A. Narachi, President and Chief Executive Officer of the
Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:



| | 1. | The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and
| | -- | ---------------------------------------------------------------------------------------------------------------------



| | 2. | The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.
| | -- | ----------------------------------------------------------------------------------------------------------------------------------------------------



|                      |  |                                                                                      
|--------------------- |  | -------------------------------------------------------------------------------------
|Dated: April 29, 2016 |  | /s/ Michael A. Narachi                                                               
|                      |  | Michael A. Narachi                                                                   
|                      |  | President and Chief Executive Officer
(principal executive officer of the registrant)

In connection with the Report, I, Stephen A. Moglia, VP, Chief Accounting Officer of the Company, certify, pursuant to 18
U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:



| | 1. | The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and
| | -- | ---------------------------------------------------------------------------------------------------------------------



| | 2. | The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.
| | -- | ----------------------------------------------------------------------------------------------------------------------------------------------------



|                      |  |                                                                                            
|--------------------- |  | -------------------------------------------------------------------------------------------
|Dated: April 29, 2016 |  | /s/ Stephen A. Moglia                                                                      
|                      |  | Stephen A. Moglia                                                                          
|                      |  | VP, Chief Accounting Officer (principal
financial and accounting officer of the registrant)

The foregoing certifications are being furnished solely to accompany the Report pursuant to 18 U.S.C. § 1350, and are not
being filed for purposes of Section 18 of the Securities Exchange Act of 1934, as amended, and are not to be incorporated by reference into any filing of the Company, whether made before or after the date hereof, regardless of any general
incorporation language in such filing. A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff
upon request.



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