Shaw appeared to have struck his head against Carvajal's body, forcing him down to the ground where he received treatment, including oxygen.
A statement from the Football Association read: "Luke Shaw remained at St. George's Park today for further rest and monitoring having sustained concussion against Spain yesterday".
Gareth Southgate announced that Luke Shaw was okay despite what seemed like a horrifying injury, and since then Mata has responded with a blog post on his website, entitled "Get well soon, Luke".
"I'm a fighter so I will be back 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. Good sign after what looked to be a very scary fall.More news: Apple expected to unveil bigger, pricier iPhone on Wednesday
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The Manchester United defender replied Carvajal message, acknowledging there was no malicious intent from Carvajal and that it was just a collision caused by a loose ball.
Shaw has made a stunning comeback to form this season and has arguably been Manchester United's best player in their opening four games.
Speaking to reporters ahead of England's friendly with Switzerland, Southgate said: "All being well, he [Shaw] has a mandatory six- or seven-day period [of not playing following the concussion]".
Neither man has been called up to the Three Lions' senior set-up before, with the duo promoted from England's Under-21s.
Left-back Chilwell replaces Shaw while forward Gray could replace United's Marcus Rashford who also picked up a knock against Spain.