Graham, who was forced off with the injury against Fulham in midweek, will have a minor operation to cure the problem.
Speaking after the 2-2 draw with Preston, boss Tony Mowbray said: "He came off with a sore groin at Fulham and it’s still sore.
"I think the plan is to have a little procedure on it - the medical department think they know what it is, it is maybe 10-days recovery period so he might not be ready for the next game as well.
"We will wait and see, hopefully he gets it sorted out and he can help us in the last few games.
"It’s not a major operation, it’s not going to finish the season for him, it’s a 10-day recovery period I think."