The bomb, equivalent to 400 grams of TNT, packed with bolts and screws exploded at 22:00 Moscow time (18:00 GMT) on Wednesday in a cafe that was packed with people from the Caucasus who had gathered for a wake.
One person from Azerbaijan, who was temporarily living in Moscow, died in the explosion and ten people were injured, two of them seriously.
"The bomb was packed with bolts and screws. It is believed that the criminal entered the cafe with [the bomb] in a briefcase or manbag and left it near one of the tables," the police source said, adding that investigators were working at the scene to try and gather more evidence.
He also said that police were working on a theory that the bomb may have been directly linked to the wake, attended by 30 people from the Caucasus.
Police are currently questioning witnesses to put together a photofit portrait of the bomber, and are trying to trace a dark colored VAZ-2109 vehicle, which the suspect is believed to have driven off in.