Paterson, 23, first suffered the injury in November in the Clarets' 1-1 draw with Doncaster Rovers at the Keepmoat Stadium.
He recovered enough to make a goal-scoring return in the FA Cup fourth round win over Burton Albion last weekend, but aggravated the problem after coming off the bench in the return fixture against Rovers art Turf Moor on Tuesday night.
Scans have confirmed a tear, with manager Eddie Howe not expecting the Northern Ireland international to return this season.
"He is going to be out for about eight weeks with a slight tear, but the likelihood is he is going to struggle to play again this season," he said.
"We would like to think we could get him back, but there is clearly a problem in there and we need to make sure we address it and get it right for the lad's sake.
"He did all his rehab spot on and we gave him time to get right, but it is just one of those things that you can't give a reason for and it's just unfortunate for him."
Paterson scored 14 goals in 42 appearances for the Iron in the 2007/08 season, his only campaign in North Lincolnshire.