The Dutchman revealed the news during his first press conference as United manager this afternoon.
The 62-year-old told the gathered media: "Michael Carrick - he is injured in the last day or the day before. So that is, in my opinion, a big blow because he is an experienced player."
When asked how long the midfielder is expected to be out of action for, he said: "Much too long for me."
According to the Daily Mail, Carrick had surgery this morning after suffering damage to a bone in his left ankle.
United are yet to make an official announcement regarding the midfielder's fitness.