The midfielder had missed three games with an Achilles injury prior to this afternoon's 1-0 win over Arsenal at Old Trafford.
Carrick was able to complete a full 90 minutes today as United closed the gap on the Premier League leaders to five points.
However, he was limping badly as he left the stadium and it seems highly unlikely he will feature in the first two matches of England's build-up to next summer's World Cup finals in Brazil.
"I have been carrying the injury for a few weeks now," he said.
"I was a bit patched up to play today.
"I got through it but it doesn't look too good."
Carrick will almost certainly be joined on the list of absentees by Red Devils striker Danny Welbeck.
Although the striker was named in Hodgson's squad on Thursday, he has not featured at club level since coming on as substitute against Southampton on October 19.
Moyes has said Welbeck is suffering from fluid on the knee and as the 22-year-old was not involved this afternoon, it does not seem likely he will be released for England duty.