Scans have confirmed the openside has damaged his MCL, with Glasgow head coach Franco Smith reporting a projected recovery time of four to six weeks.
The injury means Darge faces a race against time to be ready for Scotland's Autumn Nations Series campaign which begins when they take on the USA in four weeks, on 1 November.
"He's going to have a four-to-six-week recovery time on his injury," said Smith. "It's his MCL, so it's not that serious around his knee. If you want to hurt your knee, I suppose that's the best one [ligament] to hurt, so we will see.
"I'm sure they'll work hard to get him ready for the autumn series. I'm sure that he'd going to recover for some or most of it.
"I think once the pain or the soreness is away, then usually with those injuries you can push on. I played my whole rugby career without any of those ligaments. As soon as you get the proprioception [balance and control of movement] back and the strengthening, then they usually go.
"That depends from person to person. He's quite a tough and resilient player. So for now, you shouldn't rule out anything."
Darge will miss Glasgow's next four URC games starting against Benetton on Saturday, but No.8 Jack Dempsey could get some game-time before the November Tests.
Dempsey was set for a first competitive start since the Six Nations last Friday against Sharks but he pulled up with a groin problem near the end of the warm-up, forcing his late withdrawal from the team.
"With Jack, fortunately, it's not going to be as serious as I thought originally, so that's good news," Smith said. "Hopefully we can see him before the autumn Test matches."