The 32-year-old played in United's 1-0 win over Arsenal on Sunday but withdrew from the England squad preparing for friendlies against Chile and Germany on Tuesday and his injury could keep him out until Christmas.
"We can confirm that Michael Carrick will be out for four to six weeks with an Achilles injury," said the club on their official Twitter account.
It is believed Carrick underwent a procedure on Tuesday where he had an injection to reduce the swelling around the affected area.
However, Press Association Sport understands claims that he may require an operation are wide of the mark.
Carrick has appeared in 15 of United's 18 matches this season and his absence leaves manager David Moyes short in central midfield - an area which he tried to strengthen in the summer.
Six weeks on the sidelines would take Carrick up to the Boxing Day clash at Hull meaning he misses at least six Barclays Premier League matches, two Champions League ties - one away to Bayer Leverkusen - and United's Capital Cup quarter-final at Stoke.
However, if Carrick is out for the full duration is seems unlikely Moyes will throw him straight back into action in the midst of the busy festive programme and he may not be match-fit for the Hull game or the trip to Norwich two days later.
Carrick's United team-mate Danny Welbeck also pulled out of the England squad on Tuesday as he continues to battle with a knee injury which has kept him out since October 19.
His situation will continue to be managed by United but there is no suggestion yet he will require surgery.