The 19-year-old was knocked out cold after being caught late by a powerful aerial challenge by Nuri Sahin and falling to the ground heavily during the friendly at the Lincoln Financial Field on Saturday night.
Medical staff rushed on amid some urgent signals from players of both sides and McGeouch was carried off wearing a neck brace after more than five minutes of treatment.
And Celtic later announced on Twitter: "Dylan McGeouch has been taken to hospital with suspected jaw fracture."
A useful workout for an under-strength Celtic was overshadowed by the second-half injury to McGeouch, who had impressed with some composed possession play in right midfield, and other fitness problems for manager Neil Lennon.
Lennon lost striker Anthony Stokes, who has been suffering with an ankle problem, in the warm-up, and fellow striker Daryl Murphy limped off during the first half.
There was a minor scare late in the game too when defender Thomas Rogne needed treatment for what looked like a thigh problem.
Real won comfortably with goals in each half from Jose Callejon and Karim Benzema but Celtic were up against a strong Real squad who had put five goals past both Los Angeles Galaxy and AC Milan on their US tour and were able to bring on top internationals during the second half.
Lennon was without the likes of Fraser Forster, James Forrest, Scott Brown, Georgios Samaras and Victor Wanyama while Gary Hooper remained on the bench. Youngsters Callum McGregor and Marcus Fraser both came on.
Celtic started brightly and Beram Kayal made a strong burst forward but shot against a defender when he should have played in Kris Commons.
Cristiano Ronaldo and Kaka threatened before Callejon opened the scoring midway through the half.
Charlie Mulgrew, playing in left midfield, lost the ball and, with Kelvin Wilson dragged out of position, Xabi Alonso found Gonzalo Higuain in space on the edge of the box.
Rogne got a tackle in but the ball fell kindly for Callejon, who steered the ball out of the reach of Lukasz Zaluska and knocked it over the line.
Zaluska saved well from Ronaldo before Celtic had their best chance just before the break.
Joe Ledley made a brilliant run from inside own half, rode two challenges and turned inside a defender but fired over the bar from 20 yards.
Wilson's sliding challenge prevented Benzema converting after Ronaldo's driven cross but the Frenchman doubled the lead in the 67th minute.
Mesut Ozil won the ball just inside his own half and played a brilliant crossfield pass to Benzema, who ran into the box and shot through the legs of Adam Matthews and in off far post.
McGeouch's injury then put a dampener on the occasion and Celtic kept out Real in the latter stages.