The 25-year-old, who started twice in the RBS 6 Nations against France and England, damaged his knee in the 11-9 defeat at Scotstoun and was due to have a scan today.
Webb will hope it is not a recurrence of a problem that saw him undergo surgery in 2013 as he looks to regain the Wales No9 shirt from Mike Phillips against the Springboks in two-and-a-half months’ time.
The Ospreys stayed in the PRO12 play-off places after picking up a losing bonus point in Scotland but Wales outside half Dan Biggar knows the loss is damaging to their title bid, with Glasgow now favourites to finish fourth given that they are just a point behind the Ospreys and have two games in hand.
“It’s a massive blow,” said Biggar. “The boys put so much effort in and the spirit we showed was unbelievable, but at the end of the day it’s a defeat and it’s probably going to cost us.
“I’m just so disappointed: we edged ourselves in front with six minutes to go with a drop goal and then we just conceded to a bit of brilliance by Niko Matawalu.
“But they’ve still got some tough fixtures to come. We’ve got a couple of home games and a decent run-in, so we’ve got to keep believing until the end – but it’s hugely disappointing. We won’t give up until it’s mathematically over, we’ll keep fighting until the end.”
Biggar scored the only points of the first half with a penalty as Steve Tandy’s men dominated territorially but the Ospreys let two opportunities to score from close-range set-piece moves slip through their grasp.
Duncan Weir levelled the scores after half-time, and then moved Glasgow in front with a well-struck kick from out wide at a breezy Scotstoun Stadium.
However, the Ospreys fought back through Biggar again as he hit a simple penalty to level the scores before landing a fine drop goal to edge his side in front.
If there was one player capable of breaking down the Ospreys defence it was Matuwalu and, when the Fijian broke clear, his cross kick set up a scoring position for Tommy Seymour, who had the pace to touch down for the try that stole a crucial four points for Gregor Townsend and co.