Kennard, a senior slated to be a starter, is expected to be out at least 2-3 months and could miss the entire 2012 season, depending on the severity of the tear, which will be determined next week.
If the tear is severe, Kennard likely would redshirt the season and return as a fifth-year player in 2013.
Kennard's injury occurred while weightlifting, according to the source.
Kennard's loss would be a crushing blow to a USC defensive line that is already struggling with depth. He has started 18 games over the past three seasons for the Trojans, second most of any lineman on the roster. Next is redshirt sophomore defensive lineman George Uko, who has just two career starts.
Kennard, 21, already has undergone three surgeries over the past four years. He had to repair a torn ACL during his senior year of high school, then had surgery on his thumb after his freshman season and on his hip after his sophomore season.
Kennard did not return two text messages left for him Thursday.
Pedro Moura covers USC for ESPNLosAngeles.com