Stewart sustained his injury during the warm-up to the Black Cats’ trip to Middlesbrough, which ended in a 1-0 loss, and had to sit out the game.
Cirkin, meanwhile, suffered a hamstring issue during that fixture, and is set to be out for a short spell.
Mowbray revealed that Stewart is set for a lengthy spell on the sidelines, anywhere from six to eight weeks, whereas Cirkin could come back after a week or two as his complaint is comparatively minor.
The Sunderland manager also confirmed that the loss of Stewart means that his squad have to find new ways of banging in the goals and winning Championship games.
Mowbray believes that there are others within the squad who can and should step up in Stewart’s absence.
“Ross will be out for six to eight weeks – it could be a little longer, but that will depend on his rehabilitation and the way his body reacts”, Mowbray told Sunderland’s official website.
“He’s a really positive guy and we hope that he will be a quick healer, so we will take it game by game and hopefully he returns quickly.
“Dennis will be out for one to two weeks and it is as slight an injury as you will see, so he should be back in action within a fortnight.
“It is a blow [to lose Ross] and now we have to find a way to score the goals, but we will be positive and we will not be all doom and gloom about how we are going to win games and score.
“There are players within the squad who are capable of stepping up and our job is to find a way to win, so that’s what we will do.”
Stewart had been Sunderland’s most consistent performer up until the injury, recording five goals and three assists from seven games in the Championship.
