The 29-year-old 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."
It means Carrick will miss Saturday's visit to Everton, plus the home matches with Rangers and Liverpool that follow in a busy week.
However, Ferguson will have Rio Ferdinand available for the first time this season after the defender made a quicker than expected recovery from the knee injury he suffered on the first day of World Cup training in South Africa.
"Rio Ferdinand could have played for the reserves against Stockport last night," said Ferguson.
"He wanted to play but his training performances are so good I didn't see any point.
"He is in the squad. With three games this week, it is good that he is back in the fold."
Brazilian midfielder Anderson is unlikely to be involved on Saturday after picking up a slight knock on reserve team duty on Thursday night, although Ferguson does not believe the injury is too serious.
"Anderson came off with a little niggle yesterday but it is nothing serious," said the United chief.
"It is just the fact he has been out for a long time and he is just coming back.
"I don't think it will knock him back any length of time."