The striker suffered lateral ligament damage after coming off the bench in the 3-1 Premier League win over Manchester United on Sunday.
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."
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