With City 2-1 down, defender Nicky Mohan went in for a 50-50 challenge with Cooper in the 91st minute.
The referee waved play on but with Cooper staying down he halted play.
He was stretchered off minutes later after receving treatment on the pitch by the Minstermen physio before play resumed with a drop ball.
After spending the night in hospital, it was today confirmed that Mohan split Cooper's shinpad and broke his fibula bone. He is now set for a long stay on the sidelines.
The scorer of York's second goal, Peter Duffield, was returning from a broken leg last night, while forward Lee Nogan and ex-Tiger Gary Hobson were substituted with calf and hamstring injuries respectively.
Former Hull City manager and current Minstermen boss Terry Dolan said after the match: "It may give someone else a chance. We are disappointed by the injuries and we'll have to wait and see how bad they are."
He added: "All things considered, I thought it was a magnificent performance from the players."