In the 47th minute of the contest, the left-back was retreating toward the sideline to track a long ball hit by Sergio Ramos and slammed into Carvajal. Falling forward, Shaw's head appeared to strike the turf.
Shaw was down for several minutes as he was attended to by the medical staff, during which time an oxygen mask was applied.
The defender was eventually loaded onto a stretcher and carted off the field with Danny Rose inserted as his replacement.
"He took one on the initial challenge, but it looked like his head then struck the ground as he fell," Gary Neville said on Sky Sports.
"It was a double impact.
"The initial challenge was clumsy, but it was the fall to the ground that caused Luke Shaw the big problem."
Posting on Twitter, the player wrote: "Thank you for all the love and support I am doing fine and am in the best hands. I'm a fighter so I will be back soon."
Manager Gareth Southgate, meanwhile, indicated that no risks will be taken over the former Southampton man.
"He's sat up in the dressing room and talking and seems fairly comfortable," he said. "We'll have to assess him overnight and tomorrow.
"It's difficult to tell whether he was unconscious. We'll go through some tests. It was a nasty fall and collision. We won't take any chances with his health."
The left-back had undergone an early season renaissance with Manchester United after struggling to maintain a place in Jose Mourinho's side.
This season, he has been one of the few players consistently earning plaudits in an up and down start for the Red Devils.
Mourinho was on hand to see Shaw's good times continue in the early going of the match against Spain, as he picked up an assist on Marcus Rashford's opener which gave the Three Lions an early edge.
On Shaw's overall display as he won a first international cap for 18 months, the England manager added: "It's a great contribution for the goal and it's a big thing. We've thrown him in after a few games of the season.
"We've got quite a few players who are short of fitness and short of a bit of sharpness. To come into a game like that after so long out of the international scene is as tough a test as you can have
"That balance of having a left footer, with him and Danny [Rose], was an advantage in several situations."
Goals from Saul and Rodrigo saw Spain move back on top in the clash at Wembley, which finished 2-1.