Kean had to be taken from the field in the first half at Cardiff after suffering the knock and Rovers went on to lose the game 3-0.
The 22 year old was replaced by on-loan Gregorz Sandomierski; he is also expected to remain between the sticks for the final five games of the season.
The injury blow has come at totally the wrong time for Gary Bowyer who is still looking for his first win since taking over the hot seat for a second time this term.