Hollis, who has recently shaken off an ankle injury to reclaim the No 1 spot at Fir Park from Faroe Islands keeper Gunnar Nielsen, suffered the injury in the first half of the 3-3 draw at Easter Road.
Despite playing on for the remainder of the game, the 28-year-old is now looking at a minimum four-week lay-off and boss Stuart McCall admits it's a huge blow for the keeper.
Speaking in the Evening Times he said: "Lee could be out for anything up to a month. The injury happened early on against Hibs and it says a lot about him that he played on for the rest of the match and produced some fantastic saves into the bargain.
"But unfortunately a scan revealed the extent of the injury and I really feel for Lee. He has not had his injury problems to seek of late but he has shown a fantastic attitude to get back."
Nielsen looks certain to be reinstated for Wednesday's home game against Inverness, a team McCall expects to provide a tough test despite the memory of Sunday's League Cup Final defeat to Aberdeen being fresh in their minds.
"After the two heavy defeats at the hands of Celtic and Dundee United, Inverness have been really solid," he said.
"Both against Hibs in last midweek and against Aberdeen, when I thought they were excellent defensively in the League Cup final, they have been so well organised.
"Obviously it is always disappointing to lose a cup final on penalty kicks and you don't know how they will react but Yogi (Inverness boss John Hughes) looks like he is really putting his stamp on them now and you can bet he will have lifted them and got them motivated for Wednesday."