The Buckeyes (10-2) play Wisconsin (12-0) on Saturday at 8 p.m. ET in Indianapolis.
Barrett said he was hit on the right knee, perhaps by a photographer, while on a crowded sideline before Saturday's game at Michigan. That aggravated a meniscus injury that he has been playing through, but the knee locked up in the second half and he was unable to continue.
"He's doing a nice job with all the rehab," Meyer said.
Redshirt freshman Dwayne Haskins came in and led three scoring drives in the 31-20 victory over the Wolverines. Haskins completed 6 of 7 passes for 94 yards, also rushing for 24 yards.
As for Barrett's potential mobility on Saturday, Meyer said, "It's too early to tell. That's what this week's for. But those are all things we've taken into consideration."
Barrett, a senior, has completed 217 of 328 passes for 2,728 yards, with 33 touchdowns and seven interceptions this season. He has rushed for 672 yards and nine scores.
Barrett has 102 career passing touchdowns and 40 rushing touchdowns.