The striker suffered lateral ligament damage after coming off the bench in the 3-1 Premier League win at Stamford Bridge on Sunday.
Samuel Eto'o was preferred to Torres in Mourinho's starting line-up, and he justified that selection by scoring a hat-trick against the champions.
The Spain international's absence will leave Mourinho with just Eto'o and Demba Ba as his only fit strikers, but the performance of Cameroon international Eto'o was a major boost for the Portuguese.
The Chelsea boss told Sky Sports: "At the moment we lose Fernando for a few weeks, he has a problem with his lateral ligament. For a few weeks now we will have Demba and Samuel and hope they can do the job for us."
He added: "Of course I love when one of my players (Eto'o) becomes a special player in the match.
"Torres is dangerous in space. United came here to be compact so I picked Eto'o for his movement in small spaces."
It was another memorable afternoon for Mourinho, who achieved the landmark of winning 100 Premier League games quicker than any other manager.
Eto'o scored twice in the first half and completed his hat-trick just after the break to heap more misery on United, who pulled a late goal back courtesy of Javier Hernandez before captain Nemanja Vidic was sent off for a challenge on Eden Hazard.
The former Real Madrid coach expressed his pride at bringing up a century of top-flight wins in only 142 games, but securing three more precious points in the race for the title gave him greater satisfaction as Chelsea cut the gap to leaders Arsenal to only two points.
He added: "More important than anything is the three points. Of course it's nice (100 Premier League wins), it's obviously one more fantastic thing for my career, but most important is to win a difficult match.
"It was too hard for them to be losing 2-0 at half-time, because they started stronger and better than us. Second half we started stronger and were better for long periods.
"Overall we deserve the three points and they are three important points, because it opens a gap between us and Manchester United and Liverpool. We also close the gap on Arsenal and (Manchester) City."
