The Dnepr rocket lifted off from the Baikonur Cosmodrome in Kazakhstan, but fell to the ground about 25 kilometres south of the launch facility, the Russian news agency Interfax quoted Yuri Nosenko, the Russian space agency deputy-chief, as saying.
He said there was no damage or injuries on the ground.
A mission control official said that preliminary information indicated that a problem occurred when the rocket's third stage detached.
RIA-Novosti and ITAR-Tass reported that the engine shut off 86 seconds into the flight.
The launch of a rocket carrying a European weather satellite was postponed indefinitely last week because of a problem discovered minutes before liftoff.
Russia's space programme has suffered several embarrassing failures over the past year, jeopardising its hopes of earning more revenue from commercial launches of foreign satellites.