Woodhead suffered the injury in the first quarter of the Charger's win over the Buffalo Bills on Sunday.
The 5-foot-9, 200-pound Woodhead rushed for 38 yards on 15 attempts over three games this season. In 2013, Woodhead recorded 429 rushing yards and two touchdowns.
The 29-year-old is listed as the No. 2 running back on the Chargers' depth chart.
The Chargers (2-1) host the Jacksonville Jaguars on Sunday.