A woman and a man, who worked as church officials, were injured in the explosion as they moved a suspicious-looking bag, which had been left at the entrance of the St. Nicholas church.
"Police officers detained three young people, aged 18-19, suspected of committing the crime in the Zagorye village [west of Moscow] on Saturday," the spokesman said.
Police seized lead oxide and aluminum powder, the ingredients used to make a home-made device, during searches of the suspects.
Investigators believe the attack was a random act of hooliganism without a real motive.
The police have not ruled out that the suspects may also be involved in a blast which occurred on a railroad in southern Moscow on November 4. No one was injured in the explosion, the equivalent of 1.5 kg of TNT, which damaged rails and overhead electricity lines.