The left-back suffered the concussion in an accidental clash with Dani Carvajal during England's 2-1 loss to Spain on Sunday. Shaw was knocked out before he hit the ground and was stretchered off the field with oxygen.
"You never like to see an incident like that, that you can see is immediately potentially serious," England manager Gareth Southgate said as his side prepare to face Switzerland in a friendly on Tuesday.
"He was obviously knocked out before he hit the floor. Our medical team dealt with that really well I think. He's spent the last day with us for some recovery and he has gone back to his club this afternoon
"All being well, he has a mandatory seven-day period that he has to serve with the concussion, but he should be back in the fold as soon as that's done."