The Spain international was replaced after just 11 minutes of his side's 4-0 victory in Romania on Tuesday night and underwent tests at the club's training ground in Cobham on Wednesday.
Torres was already banned for the Norwich game in the Premier League this weekend as he serves a one-match ban for his red card at White Hart Lane last Saturday.
A statement published on Chelsea's official website read: "Chelsea Football Club can confirm Fernando Torres suffered a medial collateral ligament injury to his left knee in the Champions League group game at Steaua Bucharest on Tuesday evening.
"The 29-year-old will be out for approximately three weeks."
Following the international break, Chelsea's next Premier League game comes against Cardiff on 19 October.
Jose Mourinho's men then travel to Schalke on Champions League duty the following Tuesday before hosting Manchester City on Sunday 27 October.
Spain are joint-top of their World Cup qualifying group with France and have games against Belarus and Georgia in the next two weeks, fixtures that Torres will also sit out.
Former Chelsea boss Andre Villas-Boas, meanwhile, says the Football Association's decision not to punish Torres for scratching Jan Vertonghen is "a disgrace".
Torres was sent off during Saturday's 1-1 draw with Tottenham, but neither of his two bookings was for laying his right hand on Vertonghen's face.
Television replays appeared to show Torres digging his nails into the Spurs defender, but the FA said it was powerless to sanction the striker despite a summer amendment to its disciplinary procedures.
Under the new rules, retrospective action can be taken on incidents seen by match officials when those officials "are not in a position to fully assess a 'coming together' of players."
The FA's explanation for not charging Torres was that "one of the match officials saw the coming together of the two players, albeit not in its entirety."
That verdict has stunned Villas-Boas, who said: "It's extremely difficult to know where to start.
"Obviously, it is almost a farcical decision. It doesn't matter to me which player or club is involved.
"Neither do I want to with my words put into question Fernando's integrity; neither their manager's, in trying to defend what is our position.
"I think the FA has made a decision almost a joke. It looks incredible. How can you see the images, pretty clear, and come out without punishment, on something which overtakes all professional behaviour?
"I think the decision is a disgrace. If the committee can't solve such clear images I don't think it sets out a good first example.
"I think the FA has lost all opportunity to put some sense into the images everybody saw."