Saban reiterated the injury -- a sprained AC joint suffered during the Saturday win over Arkansas -- is not expected to have long-term ramifications.
As far as when Young resumes throwing, Saban said, "I can't tell you if that's going to be today, tomorrow or the next day."
Alabama, which passed Georgia to take the No. 1 spot in the AP poll over the weekend, hosts Texas A&M on Saturday.
The Aggies upset the Crimson Tide at home last season.
Young won the Heisman Trophy last season and is in contention to be the top quarterback in next year's NFL draft.
A junior, he has thrown for 1,204 yards and 14 touchdowns with three interceptions. He has also rushed for three scores.
Saban said he would encourage Young to avoid high-risk plays. Young injured his shoulder scrambling against Arkansas.
"The only thing I would tell Bryce is, 'Don't put yourself in a bad position,'" he said.