The winless Lions have already lost Daniel Rich for the year and will now be without their number one big man for the nearly the entire season.
Leuenberger had surgery on Tuesday morning to repair the lateral meniscus in his right knee.
The injury means former Cat Trent West will have to lead the ruck.
Stefan Martin is another who can provide support, although he has been battling a back problem and is yet to play a senior game this season.
After that, the Lions only have untried rookies on their list.
"It's obviously an extremely disappointing setback for Matthew," Lions general manager of football operations Dean Warren said.
"He is an integral part of our side and a strong on-field leader and we will definitely miss his presence.
"We have lost a wealth of experience due to injury over the last few weeks, so to lose Matthew for an extended period of time will challenge our depth.
"We are certain Matthew will approach his rehabilitation with absolute professionalism and that the rest of our leaders will step up in his absence."
In another blow, gun defender Pearce Hanley will be out for at least two weeks with a hamstring strain.