The England midfielder sustained the injury during training earlier this week and will sit out a string of games as new manager Louis van Gaal starts his reign at Old Trafford.
The Dutchman revealed the news during his first press conference, admitting the loss of one of United's long-serving players was an early 'blow' to his preparations.
“Michael was injured the day before and that's a blow for me because he's experienced,” he said. “It's very important we have experienced players.”
Carrick will be absent as United’s squad depart on Friday for their tour of the United States, where they will take part in games against LA Galaxy, AS Roma, Inter Milan and Real Madrid.