Brown is set to undergo another operation on his ankle injury while Maloney has been struggling with an Achilles problem.
Brown has beens truggling with the ankle problem for a while, but the club hoped rest might resovle the problem.
But during a visit to a specialist in Holland this week the Scotland internaitonal was told he requires a new operation.
“Scott has been to Amsterdam to see a specialist,” said Celtic manager Mowbray.
“We have come to the conclusion where we go now.
“Scott will have a minor procedure in Amsterdam which will hopefully clear up his problem. Ultimately we need to get it sorted.
“The specialist who is overseeing Scott is looking at him being out for six to eight weeks. Maloney is also out for the same length of time. There will be no surgery, just a course of injections.
“He has played with discomfort and he needs to sort it out now.”
