The striker suffered lateral ligament damage after coming on as a second-half substitute against Manchester United, though the manager has faith Demba Ba can step up.
Torres' absence will leave Mourinho with just Samuel Eto'o and Demba Ba as his only fit first-team strikers, but the manager confirmed that the Spain international is his only fresh injury concern.
"He is the only one [out]," Mourinho told reporters. "One month, or three weeks, something like that."
Mourinho previously hinted that the injury to Torres has scuppered a potential Janauary exit for Demba Ba, who has started just two league games this season.
"Now we lose Fernando for a few weeks with something in his lateral ligament [in his knee] and that is why we have Demba in the squad," said Mourinho. "We decided not to open the door to him [to leave] because he is a good player and we need him. The next few weeks is Demba and Samuel and I hope they do well for us.
"It's time for Demba. It's a pity because [Torres] is in a good moment, but it's time for Demba. Demba had a fantastic week, [it was] very difficult for me to leave him out of selection because he worked very, very well."