The midfielder lasted just 16 minutes of Wednesday night's 1-0 extra time defeat to Merseyside rivals Everton at Goodison Park.
His availability for the first leg of the Champions League last-16 tie with Real Madrid in the Bernabeu on February 25 is now in serious doubt.
"A scan has confirmed a tear in the hamstring of Steven's left leg. He will be out of action for about three weeks," said a club spokesman.
Reds boss Rafael Benitez now expects others to step up to cover his absence.
"He is an important player for us. It is always more difficult to play without him," Benitez said.
"You can't change things so it is better to concentrate on the next game.
"We have some problems with injuries and Portsmouth will be tough so we need players with fresh legs."