The Art Sherman-trained colt was due to run in Wednesday's Prince of Wales's Stakes.
The four-year-old narrowly missed out on a 2014 US Triple Crown, winning the Kentucky Derby and the Preakness Stakes before finishing a close fourth in the Belmont Stakes.
He has been lodging at the Newmarket base of trainer Rae Guest.
"We don't know how he did it," said Guest. "It is a shame for everyone involved as he had been working really well."
"California Chrome's absence is a blow for the famous fixture.
"With his brilliant race-record in America and romantic back story - cheaply bred by two 'regular guys', trained by a small-time veteran and the winner of nearly £4m to date - he would have been one of the biggest draws.
"It's a huge disappointment after all the efforts to get here, but the problem is relatively routine and shouldn't affect him long-term, just at Ascot."
Star American horse California Chrome has been ruled out of Royal Ascot because of a foot abscess.