The department said the man's nationality was not clear.
The bomb went off Monday morning at the sprawling Cherkizovsky market in northeast Moscow, where many Asians work. Fifty-five people were injured when the explosion went off.
Four victims have already left hospital, but 30 are still undergoing treatment, according to the department.
Seven patients remain in critical condition, one is in serious condition, and the condition of another 10 victims is described as moderately serious. The other 12 patients are already in satisfactory condition, the department said.
Three suspects, including two chemistry students at a Moscow institute, have been detained in connection with the explosion.
The alleged bombers have confessed they were motivated by racial hatred. As with most markets in Moscow, many traders at the Cherkizovsky market are from the North Caucasus region and former Central Asian Soviet republics, as well as China and Vietnam.
Racist sentiments have spread among Russian young people in recent years, resulting in a growing number of attacks on dark-skinned foreigners. Human rights groups have expressed alarm as police and courts continue to treat such cases as hooliganism, rather than ethnically motivated crimes.