French striker Fortune has not played since he injured his knee in the Champions League play-off defeat by Arsenal at Emirates Stadium just over a fortnight ago.
Mowbray, who picked up the Clydesdale Bank Manager of the Month Award for August at the club's Lennoxtown training camp this afternoon, said: "The prognosis at the moment is six to eight weeks and it's two weeks after the Arsenal game where he was injured in the first half. He hasn't had an operation; it will settle down.
"We were aware of it at the interval but he wanted to stay on and adrenaline gets players through. But after the game, the soreness comes. He will go through a period of rehabilitation and will get back to full fitness.''
Mowbray quashed speculation he is set to sign French midfielder Guillaume Beuzelin, who played for a Celtic XI in the 1-0 friendly win at Cork City on Wednesday night.
A free agent since leaving Coventry, Beuzelin is available outside the transfer window and has been training with the Hoops.
But Mowbray, who had Beuzelin under his charge at Hibernian, said: "We are facilitating Guillame by allowing him to train with us and he goes with Neil Lennon's group. I heard he was supposed to sign for us but I suggest that isn't the case.
"He is a lad that I respect immensely and I am amazed that he hasn't got a club yet. It's sad that talent isn't recognised and other qualities are put in to a higher pecking order. But we have some players on the fringes and we have other players like Barry Robson coming back.
"So I don't see it as an option for us to bring Guillaume in; he would become another player like those who would overload us in the midfield position.''