EXHIBIT 31.1

CERTIFICATION PURSUANT TO RULES 13A-14(A) AND 15D-14(A)

UNDER THE SECURITIES EXCHANGE ACT OF 1934, AS AMENDED

I, Adelene Q. Perkins, certify that:

1. I have reviewed this quarterly report on
Form 10-Q of Infinity Pharmaceuticals, Inc. (the Registrant);

2. Based on my knowledge, this quarterly
report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period
covered by this quarterly report;

3. Based on my knowledge, the financial statements, and other financial information
included in this quarterly report, fairly present in all material respects the financial condition, results of operations and cash flows of the Registrant as of, and for, the periods presented in this quarterly report;

4. I am responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e)
and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the Registrant and have:

(a) designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under my supervision, to ensure that material information relating to the Registrant,
including its consolidated subsidiaries, is made known to me by others within those entities, particularly during the period in which this quarterly report is being prepared;

(b) designed such internal control over financial reporting, or caused such internal control over financial reporting to
be designed under my supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;

(c) evaluated the effectiveness of the Registrants disclosure controls and procedures and presented in
this quarterly report my conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this quarterly report based on such evaluation; and

(d) disclosed in this quarterly report any change in the Registrants internal control over financial reporting that
occurred during the Registrants third fiscal quarter that has materially affected, or is reasonably likely to materially affect, the Registrants internal control over financial reporting; and

5. I have disclosed, based on my most recent evaluation of internal control over financial reporting, to the Registrants auditors
and the audit committee of the Registrants board of directors (or persons performing the equivalent functions):

(a) all significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the Registrants
ability to record, process, summarize and report financial information; and

(b) any fraud, whether or not
material, that involves management or other employees who have a significant role in the Registrants internal control over financial reporting.

|                       |  |  |  |                                                                                                               
|---------------------- |  |  |  | --------------------------------------------------------------------------------------------------------------
|                       |  | 
|Date: November 9, 2010 |  |  |  | /s/ Adelene Q. Perkins                                                                                        
|                       |  |  |  | Adelene Q. Perkins President and Chief Executive Officer (Principal Executive and Principal
Financial Officer)