The 32-year-old had to be withdrawn after badly twisting his ankle during extra time of the Capital One Cup semifinal, second-leg clash with Sunderland on Wednesday night.
The injury was still too badly swollen on Thursday for a forensic diagnosis to take place at the club's Carrington medical center, meaning the player has been scheduled for further tests on Friday morning.
It is expected that the injury will keep Carrick out of action for a month.
It is another injury blow to the England international, having already missed more than a month this season with an ongoing calf problem.
It also leaves Red Devils boss David Moyes increasingly short of midfield options, despite the imminent arrival of new record signing Juan Mata.
However, Marouane Fellaini's return to training this week has provided the Scot with some welcome relief in the midfield area, while attackers Robin van Persie, Wayne Rooney and Ashley Young are also well on the road to recovery.
United faces Cardiff in the Premier League in its next game on Tuesday, with Moyes hoping to get back to winning ways following two disappointing results against Chelsea and Sunderland in the league and cup, respectively.