A statement on the FA's official website said Carrick is suffering from a hip injury and will not join Roy Hodgson's squad ahead of the match at Wembley. Carrick is the second player to pull out of the squad after Tottenham announced striker Jermain Defoe will miss the fixture with an ankle problem.
The FA added that no replacements have been called up for either player at this time.
Carrick played the full 90 minutes of United's 1-0 victory at Fulham, while Defoe was substituted in the first half of Spurs' victory at West Brom when he landed awkwardly on his left ankle. Manager Andre Villas-Boas said Defoe would be sent for a scan to determine how bad the damage is.
"He rolled his ankle," said the Portuguese. "He will have to have a scan to reveal the extent of the injury. Hopefully there is not a lot of ligament damage. If there is, he could be out for two to three weeks."
Liverpool striker Daniel Sturridge is also a doubt for England after sustaining a thigh injury in Sunday's 2-2 draw at Manchester City. The 23-year-old, who has just four senior caps, scored a brilliant goal at the Etihad Stadium to make it 1-1 in the first half but then picked up a knock.
He remained on the pitch until he was substituted just before the final whistle but Reds boss Brendan Rodgers is not optimistic about his chances of joining up with England.
"He got a knock just before half-time on his thigh and he wanted to give it a go in the second half," said Rodgers. "I think he will be a doubt for the game on Wednesday, which is unfortunate because he was terrific.
"He is just with the medics at the moment and he will have a chat with our doctors and he will speak with the England set-up.
"They might want to have a look at it but at the moment he is obviously struggling."