Carrick out of England squad
Carrick sustained the problem - described as "minor" in a Football Association (FA) statement - in training on Wednesday.
The 33-year-old has returned to United and will miss England's Euro 2016 qualifier against Slovenia on Saturday and next week's friendly with Scotland.
The FA also announced that no-one will be called up to replace Carrick "at this time".
Carrick only returned to action for his club earlier in November after missing the first few months of the season following ankle surgery.
The former Tottenham man has not played for England since their 2-0 World Cup qualifying victory over Poland at Wembley last October.