Anderson was stretchered off at the final whistle against Derby
Manchester United will be without Anderson and Jonny Evans for three weeks because of ankle injuries.
Midfielder Anderson, 20, and defender Evans, 21, were both stretchered off during United's Carling Cup win over Derby on Tuesday.
"Anderson went for a scan and there is no break," said Sir Alex Ferguson. "But there was some ligament damage. We think he will be out for three weeks.
"Jonny Evans will also be out for three weeks," added the United boss.
Rafael and Nani were also injured against the Rams and Ferguson confirmed that they will be missing for United's FA Cup clash with Tottenham on Saturday.
Right-back Rafael was forced off just before half-time at Old Trafford and it is thought he could be missing for up to a month, while Nani suffered a groin injury and will be out of action for a week.
"The ones who are out (for the Spurs game) are Rio Ferdinand, Anderson, Nani, Rafael, Patrice Evra, Wayne Rooney, Wes Brown, Jonny Evans and Ji-sung Park," added Ferguson.
"We still have Dimitar Berbatov, Carlos Tevez and Cristiano Ronaldo fit. But we will have to call on some young players."
Ferdinand has been sidelined with a back problem since the Club World Cup tournament in Japan last month, while Evra damaged his foot in the 3-0 win over Chelsea on 11 January.
Brown has not featured for United since 25 October because of an ankle problem, Rooney suffered a hamstring injury in the 1-0 win against Wigan and was ruled out for three weeks and Park also has a hamstring problem.
Despite the injury crisis Ferguson has ruled out the possibility of bringing in any new faces during the January window, while he also said the amount of games clubs face at this time of year does not help the situation.
"I do have options," said the Scot. "Hopefully Gary Neville will be OK, then I can play Darren Fletcher at right-back, so with Nemanja Vidic and John O'Shea we would have an experienced back four.
"Alternatively, if we thought Richard Eckersley or Fabio could be one of the full-backs Fletcher can play in midfield."
He continued: "We are not the best position because there are a lot of games in January.
"At this time of year players often carry little strains, which eventually become injuries that force them to miss games.
"That is why managers for years have pursued the hope they will have a winter break. Unfortunately, it is not to be."
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