Peters, 30, suffered the injury on March 27, the team said in a statement.
The Eagles acquired Peters in a trade with Buffalo for three draft picks before the 2009 draft. He has been named to every Pro Bowl since 2007.
He played five seasons for the Bills, 3½ as a starter.
According to Dr. Michael Kaplan, ESPN's medical analyst, Peters' ankle likely would be immobilized for two to four weeks, and he would undergo physical therapy for motion and strengthening for several months. He likely will miss a minimum of four to six months of football activity.
Surgery to repair the tendon is scheduled for the Rothman Institute in Philadelphia and will be performed by Dr. Steve Raikin.
Undrafted out of Arkansas, Peters is a 6-foot-4, 340-pound native of Queen City, Texas.
Information from The Associated Press was used in this report.