Keane has not trained all week and will be assessed before the lunchtime kick-off in Govan.
Defender Edson Braafheid did not train on Friday either due to a calf injury and stopper Jos Hooiveld is still out with a hamstring injury.
Mowbray said: “I am not going to tell you what Robbie’s injury is but he hasn’t trained all week.
“I wouldn’t want to say how big a blow it is or could be because we hope he will be fit but we will wait and see.
“I will give the injured players as long as we can.
“They will have to train on Saturday and have no reaction when they wake up on Sunday morning, so we will wait and see.”
Aiden McGeady and Darren O’Dea return from suspension while Glenn Loovens has a chance after recovering from a hamstring injury.
Celtic (from): Boruc, Braafheid, Naylor, Loovens, O’Dea, Hinkel, Rogne, Thompson, Scott Brown, N’Guemo, McGeady, Ki, Kamara, Zhi, Fortune, Samaras, Keane, Wilson, Rasmussen, Crosas, Zaluska.