The centre-back has failed a fitness test on his back injury, despite undergoing pain-killing injections, and is likely to be replaced by youngster Jordon Forster.
Forster has deputised in central defence for the last three games - all Hibernian victories - but Tim Clancy is in contention after training this week following a month out with a groin problem.
"James is not going to make it," Hibs boss Pat Fenlon said. "He hasn't done enough, training-wise. We were trying to give him a chance to get himself right but it was clear that's not going to happen.
"Losing your captain is a big blow but we've got players there. We will just have to get on with it.
"These things happen in football. It's more of a blow for James, it's hard for him to take, to miss the cup final. We've got to make sure that we give him a chance to enjoy it after if we can."
Hibs are underdogs for the final, but will arrive at Hampden undefeated in six games and buoyed by their semi-final victory over Falkirk when they came from three goals down to win 4-3.
Celtic will be without injured Wales defender Adam Matthews, who has failed to shrug off a hamstring complaint.
Midfielders Victor Wanyama and Beram Kayal are suspended, while defender Charlie Mulgrew (knee) and winger James Forrest (hamstring) will be assessed.
While the Scottish Cup has not been in the Easter Road trophy cabinet for 111 years, Celtic are aiming to win the competition for a record 36th time.