Arteta had to be substituted within the first 10 minutes of the match at Goodison Park having pulled up with the injury while in a chase with Sebastian Larsson.
The club are not yet able to give any further details about how long the Spanish playmaker might be out of action for.
It is the latest in a string of injury blows for Toffees boss David Moyes, who had handed Arteta the captaincy for the Birmingham game in the absence of another hamstring victim Phil Neville.
Moyes was also without Tim Cahill due to a foot complaint and Marouane Fellaini, whose ankle problem has ruled him out for the rest of the season.
Everton's next fixture is a home clash with Fulham in the league a week on Saturday.
Source: PA
Source: PA