Torres picked up a problem during the 1-0 victory over Marseille in the Champions League on Wednesday and had to be assessed on Thursday.
Fabio Aurelio has also been ruled out for two weeks with a calf injury.
“Fernando has a strain in his right hamstring and will be out of action for between two and three weeks,” a Liverpool spokesman confirmed on the club’s official website.
“Fabio has a calf strain in his left leg and will be out for two weeks.”
