Koetter made the announcement after doctors examined the results of an MRI on Winston's right shoulder.
Winston did not play in the second half of the Bucaneers' 30-10 loss to the New Orleans Saints on Sunday after landing on his right shoulder following a tackle.
It will be the first missed start for Winston, who started all 40 games since the Buccaneers used the first pick of the 2015 National Football League draft on him. Since his initial injured, the Bucs (2-6) have suffered three straight defeats to extended their losing streak to five matches. The AC joint sprain has caused Winston to miss practice time ever since, typically preventing him from throwing most days leading up to games.
After a 384 yard, three touchdown passing game against the Buffalo Bills, Winston threw for 210 yards and no touchdowns at home against the Carolina Panthers.
The Bucs also plan to activate third-string quarterback Ryan Griffin, who is on injured reserve but can return.
Fitzpatrick, 34, completed 8 of 15 passes for 68 yards and a touchdown in relief of Winston on Sunday.