He immediately waved across the pitch to Southgate in the 86th minute and went to ground clutching the back of his leg.
After undergoing medical tests, Alexander-Arnold has been diagnosed with a grade two tear of the quad and will miss Euro 2020.
England face Romania in a final warm-up game on Sunday before beginning their campaign against Croatia at Wembley on June 13.
Southgate previously spoke of the possibility of Alexander-Arnold playing in midfield and, considering his form for Liverpool at the back-end of the season, his injury comes as a major blow.
Speaking to ITV on Wednesday night, Southgate said: “It’s obviously not good to see him having to come off in the way he did, but we’ll have to assess him over the next 24 hours.
“I think (it’s his) thigh, but the medical team are still assessing it.
“We’ll just have to see, it’s not a good sign to see him walk off in the way that he did, so we’ll know more in the next 24 or 48 hours.
“We don’t know the full extent, so the last thing you want is to see him come off in the way that he did.”