The team said his status would be evaluated from week to week.
Saturday, coach Mike Pettine said it was possible Skrine could be back for the season opener against Pittsburgh.
Skrine's injury allows the Browns to take a longer look at their first first-round pick, Justin Gilbert.
The team took him eighth overall, and he missed the preseason opener in Detroit with a groin strain.
Skrine has had a very good camp, but so has Gilbert. The two are competing to see who starts opposite Joe Haden.