Coach Mike McCarthy confirmed the severity of the injury Monday, a day after the team's 30-20 win at St. Louis.
The 36-year-old Woodson broke his clavicle in the 2011 Super Bowl win over Pittsburgh. McCarthy says Woodson is nervous about his latest injury.
The Packers played without four defensive starters against the Rams. They host Jacksonville on Sunday.
"He was a little nervous about it last night," McCarthy said when he addressed reporters. "If you've seen the play, it was a very similar action as he experienced in the Super Bowl."
Woodson briefly rolled around on the turf before getting up, holding his right shoulder area.
Woodson stayed in the game for the next play, on which Bradford completed a pass to Steve Smith on fourth down. It appeared that Woodson, still in pain from the previous play, allowed fellow safety Morgan Burnett to secure the tackle.
"You saw him protecting his one shoulder," Capers said. "He kind of hit (Smith) with one shoulder and kind of walked away. So you could tell that he hurt his shoulder on that play. But I went to him in the locker room after the game and he wasn't sure. He definitely said it was when he dove to make the interception."
McCarthy said the team would give Woodson every opportunity to return this season.
With the game in hand at 30-13, Woodson did not return to the field for the Rams' final possession with 1:52 to play. In their dime defense, their six defensive backs were Tramon Williams, Casey Hayward, Jerron McMillian, M.D. Jennings, Davon House and Burnett. McMillian and Jennings had shared the nickel and dime safety job -- with Jennings getting more snaps in that role -- while Woodson had been in the game.
On the final drive, the Packers lined up McMillian and Hayward on the Rams' slot receivers. Hayward had played that slot position opposite Woodson in the dime all game to that point. McMillian worked as a slot cover man during the offseason when Woodson was not participating in the organized team activity practices.
The Packers played without defensive tackle B.J. Raji (ankle), outside linebacker Nick Perry (knee), cornerback Sam Shields (shin/ankle) and inside linebacker D.J. Smith (knee) on Sunday. Smith joined preferred inside linebacker starter Desmond Bishop on season-ending injured reserve with the knee injury he suffered at Houston. Bishop was lost for the season when he ruptured his hamstring tendon in the preseason opener on Aug. 9 at San Diego.
Asked if he thought Woodson would indeed return this season, Capers said: "Well, just knowing Charles, all I have to go on is him in the past. He's been doing this long enough that he knows his body and he's kept himself in tremendous condition or he wouldn't be playing at his age right now and be able to play at the level he's played.
The Packers cannot place Woodson on injured reserve and bring him back because they have already designated for return running back Cedric Benson, who hurt his foot at Indianapolis on Oct. 7.
"There'll have to be some other guys pick up the leadership role," Capers said. "Obviously, Charles is a leader. He's been a very productive guy on the field and that's the way you develop into a leader. I think there's an awful lot of respect for him. Now, we've got to have some other guys step up and produce."
Replacing Woodson won't be an easy task though, since joining Green Bay in 2006, he has started 100 of 103 possible games. According to ESPN Stats & Info, Woodson's nine interceptions returned for touchdowns are three more than any other defensive back in the league during his tenure with the Packers.
Information from The Associated Press was used in this report.