Winston sprained the AC joint in his right shoulder on last month against Arizona, and he landed hard on that shoulder when he was sacked in the final minute of yesterday's first half against New Orleans.
The Buccaneers have yet to reveal the exam results of the two injuries, which resulted in Winston's early departure Sunday.
This will be the first time in 40 career National Football League games that Winston will miss a start.
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A 40-yard catch from Taylor Gabriel and touchdown pass to Tevin Coleman put the Falcons back in it with about four minutes to go. NEAL WITH THE STRIPS: Falcons safety Keanu Neal had a nice first quarter, forcing Stewart's two fumbles and recovering one.
Winston has struggled for the 2-6 Bucs this year, passing for 1,920 yards with 10 touchdowns, six interceptions, and five fumbles.
Bucs coach Dirk Koetter told reporters on Monday Winston is facing a spell out of action, with Ryan Fitzpatrick to replace him as the starter against the New York Jets this weekend.
Tampa is expected to activate Ryan Griffin from injured reserve this week and would carry three quarterbacks on the roster.
"[The MRI showed] a lot of medical terms that I'm not an expert on, but he needs to be off a couple weeks".