Carrick had an injection on Thursday after informing Sir Alex Ferguson the long-standing problem was starting to bother him once more.
"He should be out for three weeks, maybe a month at most," said Ferguson.
Carrick was an unused substitute during England's recent Euro 2012 double-header but has not started a game for United since the Community Shield triumph over Chelsea at Wembley last month.
"He has had a problem with his Achilles," added Ferguson.
"It has been bothering him for a few weeks now, so we sent him to a specialist in London yesterday and he had an injection.
"We are hoping that settles it down.
"We have been considering what we should do about it. The best thing is to get it treated and out of the road now because everyone in the squad is fit."