Taylor limped off Manuka Oval during the third term of the 21-point defeat, with the Giants forced into making their tactical sub change as their star defender was left in the hands of club medical staff.
The 23-year-old will undergo scans on Sunday as GWS brace for bad news for their first-string stopper.
Giants coach Adam Kingsley suspected the setback will be a "reasonable one" for Taylor.
"I'm not sure the severity of it. It looks like a reasonable one, so we'll wait and see," Kingsley said post-game.
Sam Taylor comes from the ground with what appears to be a hamstring injury.
— Fox Footy (@FOXFOOTY) April 22, 2023
Taylor was replaced by veteran defender Adam Kennedy in the contest, with the Giants sub managing just 15% time on ground before suffering a setback of his own.
A bump from Lion Keidean Coleman near the boundary line in the final term left Kennedy with a knee complaint, with Kingsley suspecting the injury was sustained from an awkward landing from the bump.
"I couldn't really see it because it was over the boundary line when he got bumped," Kingsley said the incident.
"It must've been the way he landed. He didn't crash into the fence, I know that. So it must've been just on the landing."
The Giants will regain star midfielder Tom Green back for suspension for their Round 7 bout with arch-rivals Sydney, while recruit Toby Bedford will be in the selection mix after making his return from a hamstring injury through the VFL this weekend.
GWS sit 12th on the ladder with two wins from six matches.