Glasgow flanker Rob Harley faces up to eight weeks out with knee ligament damage, while team-mates Ed Kalman and Pat MacArthur face even longer on the sidelines.
Harley injured his knee in training last week and his club have confirmed he had suffered a lateral collateral ligament tear. The 22-year-old, who scored a try on his Scotland debut against Samoa in June, could struggle to regain his fitness in time to be considered for Scotland's autumn test series.
Scotland face New Zealand on November 11 followed by games against South Africa and Tonga.
Prop Kalman has undergone surgery on his back after suffering an injury in the pre-season friendly against Sale and is facing at least three months out of the team. Hooker MacArthur needs surgery on a fractured foot, which he suffered against Scarlets on Friday, and Glasgow say he will be missing for three to four months.
The triple blow comes as Gregor Townsend seeks his first win as Glasgow head coach following defeats by Ulster and Scarlets in the RaboDirect Pro12.
Townsend, who has made six changes for the clash with Swansea at the Liberty Stadium on Friday night, said: "We're clearly disappointed to have lost our opening two matches, and there's a determination about the whole group to achieve a win this weekend.
"To do that away from home against a quality outfit like Ospreys, we know our performance will need to be spot on in all the key areas. In both the Ulster and Scarlets matches, we've done certain things very well, but haven't been as accurate as we know we can be in other facets of the game.
"As well as ensuring we don't turn the ball over as often this week, we'll need to ensure our physicality is right up there. Ospreys have one of the most aggressive defensive lines in the competition, and they bring the same principles to the breakdown.
"We know our players are more than capable of matching that sort of relentlessness, and we're heading to Swansea with confidence."
Dougie Hall replaces MacArthur while Mike Cusack comes in at tighthead prop after Moray Low suffered a calf injury. Flanker Chris Fusaro, stand-off Duncan Weir, winger Tommy Seymour and centre Peter Horne also come in.