The former Luton player faces more than two months out after twisting his knee early in Sunday's league defeat by Hearts' Hampden opponents, Celtic.
Manager Craig Levein told the club's official website: "It's hugely disappointing news for us, and especially for Olly.
"He twisted his knee on the pitch with nobody around him on Sunday and at the time it didn't look too good, now we know that he'll be out for around 10 weeks.
"Missing out on a cup final is hard to take so Olly now has to focus on his rehab and target making a comeback for the beginning of the next league campaign.
Haring (groin) and Djoum (Achilles) have missed recent games along with striker Uche Ikpeazu, who is working to overcome a hamstring issue.
body check tags ::