The No. 10 pick in this year's draft, out of Alabama, has started every game at left tackle for Cleveland this season.
Wills was placed on the list after being identified as a high-risk close contact to somebody outside the organization. Wills would be eligible to come off the virus list if he tests negative over five consecutive days, potentially putting him on track to still play Sunday against the New York Jets.
"There's a possibility," said coach Kevin Stefanski.
Wills' absence in practice at the least is the latest blow for a suddenly banged-up Browns offensive line. Starting right guard Wyatt Teller missed Sunday's game with an ankle injury and was expected to miss practice again Thursday. Cleveland has also lost key backup lineman Chris Hubbard, who was placed on injured reserve this week with a knee injury he suffered while starting in place of Teller on Sunday. Rookie center Nick Harris filled in for Teller and Hubbard at guard.
A source told ESPN that Wills' close contact issue had nothing to do with his Winter Blast event earlier this week.
The Browns also placed receiver Ryan Switzer on the practice squad/COVID-19 list.