The injury is a fresh setback for Carrick, who had only just returned to action after three weeks out with an ankle injury sustained in United's opening game of the season against Newcastle.
He was forced to pull out of the England squad for the friendly against the Czech Republic and subsequently missed the two World Cup qualifiers against Andorra and Croatia.
Carrick's latest injury will also rule him out of England's next two qualifers against Kazakhstan and Belarus next month.
He will miss United's opening Champions League game against Villarreal on Wednesday, their second against Aalborg on 30 September and possibly their third against Celtic on 21 October.
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