He received treatment for several minutes on the field before being taken off wearing an oxygen mask.
After a clash with Spain's Dani Carvajal, the defender landed heavily on the ground and suffered a massive blow.
"Luke is awake and alert, having been assessed by our doctor and given an X-ray".
He was obviously knocked out before he hit the floor.
Shaw was walking and talking before the match was over and tweeted he was "doing fine" that night, but will now head back to United.
"I chose to spend mine back at home, to make sure that I'm feeling fully charged ahead of the games that are coming up soon".
According to Marca, the Real Madrid defender immediately sought out the player in the dressing room after the conclusion of the game, only to be told that he had been brought to hospital for an MRI. There'll be tests. We won't take any chances with his health, it was a nasty looking fall.
The sight of Shaw being surrounded by medics on the pitch brought up memories of the injury he sustained during the second season of his United career which he recently admitted nearly cost him his leg.
After struggling last season to convince Jose Mourinho he was worth a place in the team, he has started the current campaign in impressive fashion and his contribution on Saturday before his injury will have impressed Southgate.
The left-back not only returned to the worldwide fold but also started on Saturday night, creating a goal for Marcus Rashford.