Watkins started the 24-14 victory but was helped off the field late in the first half after defensive end Melvin Ingram fell on his teammate on the play. Watkins couldn't put weight on his leg as he left the field.
Watkins, 26, spent the first four seasons of his career with the Philadelphia Eagles. He signed with the Chargers as a free agent in April.
The Chargers filled Watkins' roster spot by claiming undrafted rookie safety Micah Hannemann off waivers from the Cleveland Browns.