McCown's return to the starting lineup comes five weeks after he suffered a broken left collarbone against the Baltimore Ravens in his only game so far this season.
He was medically cleared Wednesday and practiced fully for the first time since the injury. He had been doing limited work in practice the previous two weeks.
Quarterback Cody Kessler will not be available Sunday, as he remains in the concussion protocol. The other quarterbacks on the roster are rookies Kevin Hogan and Joe Callahan.
In other injury news, wide receiver Corey Coleman will miss his sixth straight game as he recovers from a broken hand. Cornerback Joe Haden is questionable versus the Jets with a groin injury.
Information from ESPN staff writer Pat McManamon contributed to this report.