Carrick played the full 90 minutes of Tuesday's 1-0 Champions League win over AS Roma but an X-ray later showed the damage.
With Owen Hargreaves already out for a month with a knee injury, Carrick's absence - which could be as long as six weeks - means United is unlikely to field the pair together again until mid-November.
That would leave United without its central partnership for Premier League games against Wigan, Aston Villa, Middlesbrough, Arsenal and Blackburn, as well as a pair of Champions League games against Dynamo Kiev.
Darren Fletcher was already ruled out until the end of October with a leg injury, so manager Alex Ferguson may need to call on defender John O'Shea or the recently acquired Anderson to play alongside the attacking Paul Scholes.
United is second in the Premier League, but is also without goalkeepers Edwin van der Sar and Ben Foster, defender Mikael Silvestre, and midfielder Park Ji-sung.
The companies involved in the implementation of the Nord Stream-2 project may deal with restrictive measures against them, a spokesman for the US Department of State said