Rodgers, who missed two series in the fourth quarter on Sunday, thinks he may have separated the shoulder.
"It felt like that's what possibly happened," the fourth-year pro said after being sacked three times and throwing his first three interceptions of the season. "But we're going to wait until tomorrow to figure out exactly what the problem is."
With the Packers leading 21-20, Rodgers was removed from the game and replaced by Matt Flynn for Green Bay's first offensive possession of the fourth quarter.
Rodgers re-entered 7 minutes later after the Bucs took a 23-21 lead on Matt Bryant's third field goal of the game.
Rodgers said he was injured in the third quarter when he scrambled on third down for a 7-yard gain. He remained in the game and threw a 48-yard touchdown pass to Greg Jennings the next time Green Bay had the ball, trimming a 13-point deficit to 20-14.
"When I threw the touchdown pass, it was pretty intense pain," Rodgers said. "I tried to throw on the sidelines and couldn't do it."
The quarterback returned with 2:26 to go. His team's hopes for a comeback faded, though, when Rodgers was hit from the blindside as he released a second-down pass from the Packers 40 and Gaines Adams intercepted near midfield.
The Bucs put the game away when Earnest Graham broke a 47-yard run to the Green Bay 1, then scored on the next play.
Flynn led the team's last offensive drive, which ended with the Packers turning the ball over on downs.
Packers coach Mike McCarthy said he had "no idea" if Rodgers will be able to play next week against Atlanta.
"It's too early to tell," McCarthy said.