Young threw his helmet in frustration, entered the medical tent and later went to the locker room. His parents left their seats in the stands to join him.
Young was able to return to the sideline, and Alabama coach Nick Saban said the injury isn't considered serious.
"I think he's OK," Saban said. "He doesn't have a serious injury. We didn't think he could go back in the game today because I didn't think he had much steam throwing the ball.
"He's had these [injuries] before and in a few days he starts to respond pretty well. So we'll just have to see how it goes and, you know, play it day-to-day."
A possible first-round pick in next year's NFL draft, Young completed 7 of 13 passes for 173 yards, one touchdown and one interception before the injury. He was on the sideline and in full uniform during the second half but did not take a snap.
Backup Jalen Milroe came off the bench and completed 4 of 9 passes for 65 yards and a touchdown. He also ran for 91 yards and a touchdown on six carries.
Milroe said Young told him, "Just to stay calm, calm, cool and collected. Just fall back to your level of training."
"We have a great bond," Milroe said.
Asked how the offense changed with Milroe in, Saban quipped, "I was gonna call Jimbo afterward and tell him," referring to Texas A&M coach Jimbo Fisher.
Alabama hosts Texas A&M next Saturday in Tuscaloosa. The Aggies upset the Crimson Tide in College Station last season.
"There's only one Bryce Young in this country and he's a great player," Saban said. "Jalen can do what Jalen does, and we have confidence in him. We have confidence in a development of Ty Simpson as his backup. But hopefully Bryce will be OK.
"But I thought the offense did a really good job of continuing to score points in a different way than when Bryce plays. And I think you got to have that kind of diversity on your team. You got to be able to win more than one way."