It means the midfielder could miss next week's Europa League final against Arsenal.
Loftus-Cheek was part of a strong lineup to face New England in a match raising awareness for antisemitism.
He was taken off after just over an hour of the game, with academy starlet Conor Gallagher coming on in his place.
ESPN FC correspondent Liam Twomey described the injury as one that would likely end his season: “I'd be very surprised if that isn't the end of Loftus-Cheek's season.
“The reason for this friendly is unimpeachable but the timing always left the possibility for something like this. Sarri was right to be worried."