The winger came off in the first half of their cinch Premiership victory at the weekend and becomes the latest player to be sidelined ahead of the Viaplay Cup quarter-final tonight against Livingston.
Rangers are still without Kieran Dowell, Todd Cantwell, Tom Lawrence, Nico Raskin and Danilo.
"Obviously Rabbi has sustained a knee injury," first-team coach Neil Banfield said at a press conference. "He's going to be six weeks. But we've got the squad all prepared for tomorrow, he's added to the injury list.
"We build a squad for tomorrow and we go again against Livingston tomorrow night."
Although Rangers secured three points against the Steelmen, the team were booed off at full-time after a lacklustre display at times and manager Michael Beale admitted post-match that his side had "got away with one".
Their performance came on the back of victory in the Europa League against Real Betis on Thursday night, but the attention now turns to Livi in the cup. Rangers are one of the favourites to win the competition after Celtic were knocked out by Kilmarnock last month, but Banfield insists this adds no pressure.
"No, there's no added pressure, the history of Rangers is winning trophies," he said. "That's what we're about and that's what this big club is about, winning trophies.
"No matter who's in it, that's what we focus on and winning in the next competition. We're in four competitions which is great, league last Sunday, Europe in the week and League Cup tomorrow.
"That's what we've all come here for and that's what we want to be involved in. We prepare exactly the same as we do every game and we're focused on winning the game on Wednesday night.
"We've prepared for this and we deal with it, again with the injuries, we know we've built a strong squad.
"It's time for the players to come into the team and take us hopefully to the semi-final, a game at Hampden Park and a semi-final if we win on Wednesday night."