Both midfielders picked up injuries in the 2-0 first-leg win in Sweden on Tuesday night.
Ahead of the trip to Inverness in the SPL on Saturday, the Celtic boss said: "Joe has a grade one groin injury and he will be out for a couple of weeks and Beram has had a reaction to his other ankle (to the one which was operated on) and he will be maybe three to four weeks."
He added: "The injuries aren't majorly concerning, particularly Joe's injury.
"Joe has been one of the best signings since I came to the club, and so consistent, he is a big loss to us.
"Beram is a little bit of a worry because it is his other ankle which is giving him bother.
"It is unfortunate. The midfield is probably the strongest department at the club.
"We have Victor Wanyama to come into the squad and we have options."
Thomas Rogne (ankle), Scott Brown (hip), Georgios Samaras (thigh) and Kris Commons (ankle) are all doubts for the game against Caley Thistle.