The Scot told reporters that the England international is struggling with a slight knee ligament problem and is facing two to three weeks out.
"It was a volley towards the end of training," said Ferguson. "He did a ligament at the back of his knee and could be out for two to three weeks."
The striker played in the 1-1 draw with Swansea on Sunday but was not involved as the Premier League leader secured a 4-3 Boxing Day victory over Newcastle United late on.
Sir Alex was also without Ashley Young with a knock, while Danny Welbeck was ruled out prior to the game through illness.