Having beaten the French side on Wednesday, Rafa Benitez's men celebrated qualification for the knock-out stage, but the Spanish forward's injury marred the victory.
The 24-year-old underwent a scan, which indicated that he needs to rest for several weeks.
"Fernando has a strain in his right hamstring and will be sidlined for between two and three weeks," A club spokesman told Liverpool's official website.
The Spanish ace has just recuperated from a right hamstring strain, having made his comeback against Fullham in the Premier League last Saturday.
Blow
Even though Torres is tipped to return within several weeks, manager Benitez said he can't determine when the hitman would be declared fit.
"You cannot guarantee when he'll be back. I was with him and the physios two minutes ago and he's already working. But it always depends on the player," the Spanish tactician said.
"It's a blow especially because we lost him before and we've been talking about the understanding between him and Robbie Keane, and him and Steven Gerrard."