BBC Sport claims that the 31-year-old picked up the problem on Tuesday while on a winter break with Spartak Moscow.
It has also been reported that Arsenal knew about the injury before signing the Sweden international on loan from Spartak on transfer deadline day.
Kallstrom told the Gunners of his problem on his arrival at the club on Friday, and a CAT scan found an issue with his back.
Although Arsenal manager Arsene Wenger was informed of the problem by the club's doctors, the Frenchman decided to proceed with the signing.
Kallstrom did not train with his teammates on Friday or Saturday and is expected to miss the Gunners' next six matches.