"Torres had no confidence and said he couldn't play (against Birmingham), so we started the treatment yesterday," Benitez said.
Related ArticlesFootballers' divesHow can David Ngog still get away with blatant cheating?Don't knock divers for having the X-FactorLiverpool dive to new depthsDavid Ngog cheated to win penalty, says CarsleySport on television"He has to work with the physios and try to improve and be ready. We are not talking about an operation at this moment.
"I don't know if he will be ready for Man City."
Albert Riera, Yossi Benayoun and Daniel Agger all also suffered knocks in Liverpool's 2-2 draw against Birmingham on Monday night.
"Riera had the same problem (hamstring) as before," Benitez said. "Yossi has the same problem as Riera.
"Some players are playing too many games in a row. They are working very hard and so you always have this risk. I think both will have tears.
"Agger also had a problem with his back. It's not serious but he felt it a little bit."
Benitez must also now deal with the fall-out from Monday's match, with angry Birmingham City players and management accusing Liverpool striker David Ngog of cheating after he earned a controversial penalty that salvaged the draw at Anfield.
With Birmingham leading 2-1, Ngog went to ground with 20 minutes remaining after a challenge by Birmingham's Lee Carsley. Television replays showed no contact had been made.
"You are supposed to be teaching your kids an example and this is just an embarrassing case of cheating," Carsley said.
"I was absolutely nowhere near him. It's a joke. I know I didn't touch him and I said to the referee to book me or send me off. That would have made me feel better."