The third-year quarterback sat out the second half of Sunday's 30-10 loss to the New Orleans Saints after being sacked late in the second quarter and landing on the shoulder he initially hurt at Arizona on October 15.
This will be the first time in 40 career National Football League games that Winston will miss a start.
Starting left tackle Donovan Smith also left the game with a knee injury.
Veteran Ryan Fitzpatrick played in the second half for Winston and finished 8-of-15 for 68 yards and a touchdown in the 30-10 loss.
Before this week, Winston had only thrown one day a week because of the injury.
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On Sunday, Winston completed 7-of-13 for 63 yards with no touchdowns or no interceptions. Tampa Bay's bye week was supposed to land in Week 11, but Hurricaine Irma pushed it up to Week 1, when the Dolphins game was rescheduled.
Jameis Winston warming up before Sunday's game at New Orleans. All in all, a bit of rest might help heal up more than just an injured shoulder.
Asked after the game if he thought he might be shut down for the season, Winston said: "I don't control that at all".
Winston injured the shoulder in Arizona on October 15th.
The Bucs are moving Ryan Griffin to the active roster as Fitzpatrick's backup.