The incident, in which seven people were injured, occurred at around 1:00 a.m. Moscow time on the Gorkovskoye highway, near the town of Balashikha to the east of the capital, in an area with several shops and cafes.
Police said that immediately after the attack, two suspects were identified. The search for the second man is ongoing.
"One of them, a local resident, left clear traces and was tracked down. He has been taken to the police station, where he is being questioned," a spokesman said.
Russian tabloid Komsomolskaya Pravda earlier reported that six prostitutes were injured in the attack, along with one client. The paper said that several men, most of whom work at a nearby military factory, had got into a dispute with pimps when negotiating a price for the prostitutes' services.
The women, from various parts of Russia and Ukraine, were standing on the sidewalk when an Opel car pulled up, and an explosive device packed with metal shards was thrown out of the window, detonating in their midst, the paper said.
Two women suffered only minor injuries, while four along with one client received severe arm and leg wounds, and are being treated in hospital.
According to the tabloid, the Gorkovskoye highway is a notorious sex destination, with clusters of prostitutes "every 500 meters".