The Brazilian, who has been plagued by injury problems all season, did not fly out with the squad for Thursday's Europa League match at Athletic Bilbao.
"Anderson could be out for four to five weeks with a hamstring injury," Ferguson told a news conference in Bilbao.
"Some hamstrings are relatively straightforward but we have to wait and see how he is in the next week or so to get a better idea."
United defender Phil Jones also missed the trip due to illness and Portuguese winger Nani has a sore foot but Ecuador winger Antonio Valencia returned to the squad after four weeks out with a hamstring injury.
United lost the home leg of the last-16 tie against Bilbao 3-2 and Ferguson is expecting another difficult match.
"They had a great motivation last week coming to Old Trafford but whether they can maintain that is difficult to say," Ferguson said. "We expect them to. We just need to step up our performance level."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.