Harris confirmed the news shortly after NFL Network's Ian Rapoport reported the injury.
It's another blow to a Chargers secondary that already lost safety Derwin James to a season-ending injury.
Harris inked a two-year deal with the Chargers this past offseason after spending the previous nine seasons with the Denver Broncos. The 31-year-old has earned four Pro Bowl selections and recorded 20 interceptions over 124 career NFL starts.
The Chargers' secondary has failed to generate turnovers during the team's first three games of the season, managing just one interception. Los Angeles will take to the road to face Tom Brady and the Tampa Bay Buccaneers in Week 4.