Bougherre did not feature in the 3-3 draw with Dundee United on Sunday, due to a hamstring problem.
“He’s out for a few weeks,” said Rangers assistant boss Ally McCoist.
“He went for a scan and it’s revealed a small tear in the hamstring, which would probably be about three weeks, hopefully less than four.
“It’s a blow but other teams have disappointments with injuries and suspensions and we’re no different.”