The 31-year old Sweden international will spend the remainder of the season with the Gunners after Aaron Ramsey suffered an injury setback.
Kallstrom, who has played 108 times for the Swedes, joined Spartak from French side Lyon in 2012 but will now suit up for Arsenal for the next four months.
Kallstrom said: "Arsenal is an amazing club with a lot of great players and a coach who has done really well here for a long time.
"I am so pleased to come here to learn as much as possible. I'm here to do my best for Arsenal and to help out the team, so we can achieve good results for the last part of the season."
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