The England international has been nursing a niggling problem for some time, but returned to action in Sunday's 1-0 victory over Arsenal.
He came through 90 minutes at Old Trafford, but revealed afterwards that he was feeling the effects of a demanding contest.
Carrick said: "I have been carrying the injury for a few weeks now. I was a bit patched up to play today.
"I got through it but it doesn't look too good."
He was forced to withdraw from the England squad for a friendly double-header against Chile and Germany as a result of the problem, along with United colleague Danny Welbeck.
Carrick could now be out of action until Christmas, with another period of recovery required to return him to full fitness.
His absence will be felt by United, as they are due to take in important fixtures at home and abroad over the coming weeks.
UEFA Champions League competition will see them face Bayer Leverkusen and Shakhtar Donetsk, while there are games to come against the likes of Tottenham Hotspur, Everton and Newcastle United in the Premier League.
United and England team-mate Phil Jones told Sky Sports News: "He's been in terrific form and he's a top player. He'll be missed by club and country.
"He's a great player, he brings a lot to a side, his range of passing, so he'll be sorely missed."
Confirmation of Carrick's injury absence comes after the midfielder acknowledged United had made a 'shocking start' to the season under new boss David Moyes.
"After a shocking start we are not in a bad position," said Carrick after United beat Arsenal 1-0 on Sunday to close to within five points of the leaders.
"We never really got too despondent. We were frustrated with our performances and results but you have to stay patient and trust yourself.
"We knew there was a long way to go and there still is."
Jones has suggested some people have been hoping for United to fail, having become jealous of their immense success under Sir Alex Ferguson.
However, Carrick does not view it in quite such graphic terms and he feels some of the criticism for their sluggish start was deserved.
"You can take it as a compliment because of what we have done over the years," he said.
"When we are not at the top, because of our recent run in the league people are asking questions and criticising.
"In some ways it is fair. In others we take it with a pinch of salt. We have to deal with it from within.
"A few weeks ago we probably didn't think we would be in this position as quickly. Now we are not in bad shape, although it is still very early."
After early season failures to beat Chelsea, Liverpool or Manchester City, Sunday's result also quashes the claim that Moyes may struggle against United's major rivals.
And that should ease the nerves of the fans who remain uncertain about Moyes being the right man to take on the unenviable challenge of replacing Ferguson.
But Carrick always felt there would be some period of transition required after such a seismic change.
"Obviously with the new manager and new staff coming together and gelling, (defeating Arsenal) helps the feeling within the club," he said.
"It is easy to jump on the bandwagon when we have lost a game or two and people are saying it is all wrong.
"We knew that wasn't the case but this result has put us in a better position and now there is a bit of stability."