Tagovailoa, who is battling incumbent Jalen Hurts for the starting quarterback job, broke a finger on his throwing hand three weeks ago. He was able to participate in a limited capacity following the injury until Saturday.
"Tua had a little setback yesterday with his hand," Saban told reporters in Tuscaloosa following the scrimmage. "Doctors are trying to evaluate the best course of action and what we do with him the remainder of spring."
Saban said he was unable to offer any further details on the injury.
"I can't really tell you any more," he said. "He didn't take any snaps today. He did take a lot of snaps yesterday. We're going to try to protect this and make sure that this thing is not going to be an issue for him in the fall."
Alabama wraps up spring practice with its annual A-Day scrimmage next Saturday.
Tagovailoa was primarily a backup as a freshman last season. In the second half of the national championship game, Saban benched Hurts in favor of Tagovailoa, who threw three touchdowns, including the game winner in overtime.
Hurts, who won SEC Offensive Player of the Year as a freshman in 2016, has compiled a record of 26-2 as a starter. He threw for 2,081 yards, 17 touchdowns and one interception last season. He also rushed for 855 yards and eight touchdowns.
Saban has said he has no timetable for when he'll make a decision about who will start at quarterback. He has even hinted at playing both during the season.