Alexander-Arnold immediately signaled to come off, and ended up being helped around the perimeter of the field by a member of England's medical staff at the Riverside Stadium in Middlesbrough. Alexander-Arnold was seen shaking his head.
"It's not a good sign to see him have to walk off as he did," Southgate told ITV television. "We'll know more in the next 24-48 hours.
"Let's see how Trent is first and then we'll go from there," the manager added.
Alexander-Arnold was one of four right-backs selected by Southgate in the 26-man squad for Euro 2020, so the team does have plenty of cover if he is ruled out.
Forward Jack Grealish also needed an ice pack after he came off in the second half but the player said it was just a bit of stress to his shin and he was not concerned.
Bukayo Saka scored the winning goal for England, which has one more warmup left -- against Romania on Sunday -- before the tournament starts.
Information from the Associated Press and Reuters was used in this report.