NFL Network insider Albert Breer confirmed the report through a league source.
News of the injury came on the same day that Sanchez was limited in practice.
"I'm in there," Sanchez said. "I'm playing, that's all there is to it. I have to be on the field. That's what I'm here for, and that's what I'm going to do."
Sanchez had an MRI exam on the shoulder Monday.
The second-year pro did mostly soft-tossing early in practice Wednesday, and even threw a few passes left-handed.
"I felt good at practice today," Sanchez said. "They kept me limited, just to be smart, but if we were playing today, I'm definitely in there. I feel good, and I'll be ready for Sunday."
Sanchez said he went through all the footwork and participated on every running play to make sure he's mentally prepared to play the Bears. He added that he "should" be able to get in a full practice before the game.
Ryan said it's a "possibility" that Sanchez's shoulder could grow worse, "but we don't anticipate it."
After struggling for a few games, Sanchez had a few practice snaps taken away from him last week. It was a move that Ryan half-kiddingly said was just to "tick him off" and give backup Mark Brunell a few plays. Sanchez said the two spoke about it.
"He knows that we have an understanding that I don't always agree with him," Sanchez said. "It's personal to me (the starting job), and I think he knows that. ... I'm possessive about this job, so we had a little talk about it, but it's good. We're both competitive, so it was good. I think part of it was a psychological thing just to kind of test me a little bit, so we're good."
Meanwhile, wide receiver Santonio Holmes didn't practice, sitting out with turf toe, but he's also expected to play.
"During the game, I guess he had a toe injury and I never thought it was that bad," Ryan said. "I never knew that we would have to hold him out today. It was bad enough to keep him out. I expect him to play, but he was not comfortable today."
Ryan added that he believes Holmes will be able to practice at some point this week and doesn't believe the receiver will be out "by any stretch of imagination." Holmes has 47 catches for 660 yards and four touchdowns this season.
Right tackle Damien Woody (right knee) will miss his second consecutive game after having arthroscopic surgery last week, and he again will be replaced by Wayne Hunter.
Defensive lineman Trevor Pryce was limited after missing a game with a hip injury. He expects to play against the Bears.
The Associated Press contributed to this report.