Winston was known to have played through a broken thumb toward the end of the year, but the meniscus injury was previously unreported.
The pivot, who led the league in both passing yards and interceptions during 2019, also had LASIK surgery this offseason to correct his vision.
The former No. 1 overall pick is scheduled to hit free agency in March. The Buccaneers are believed to be weighing the possibility of assigning Winston the franchise or transition tag, but they've also been open about wanting to upgrade at the position.