Warburton, who missed the third Lions Test last summer through injury, looks set to miss the rest of the domestic season.
The injury also appears likely to rule him out of the Wales summer tour, like fellow Lion Leigh Halfpenny, according to his head coach Warren Gatland.
"It looks like he's dislocated his shoulder and they had to put it back in after the game," said Gatland.
"It looks like he'll be ruled out for the rest of the season and probably the tour as well.
"He's being scanned tomorrow [Sunday] and the likelihood is he'll probably need an operation on that."