Spectacular footage showed the rocket veering off its trajectory just seconds after its 6.38 am (0238 GMT) launch, before erupting into a ball of flames and releasing highly toxic rocket fuel into the air.
The Russian space agency Roskosmos, citing preliminary information, said the accident caused no damage or casualties.
"It seems something is going wrong," said a television commentator during the live coverage of the launch. "Something is wrong. It seems it will be a catastrophe," said the presenter, his voice trembling.
The rocket was supposed to take three Glonass-M satellites into space.
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"A rocket carrier fell to the ground and exploded on the territory of the cosmodrome," the space agency said in a statement, adding the rocket fell on the territory of the Baikonur cosmodrome in Kazakhstan.
The agency said that during the accident, which took place 10-15 seconds after takeoff, toxic rocket fuel was released into the air.
A Roskosmos spokesman could not immediately say whether people living near the crash site were being evacuated.
Russia has suffered several recent setbacks in its space programme, notably losing expensive satellites and an unmanned supply ship to the International Space Station.