The bomb went off at 1902 IST in the baggage claim area of the international arrival sector, Itar-Tass quoted Tatyana Morozova of the Russian investigation committee as saying.
Russian news agency Ria Novosti said at least 31 people were killed in the explosion that rocked the airport.
Airport employees broke down the wall between the main airport and the arrival zone to allow passengers to escape from the scene of the destruction, it said.
According to Business FM radio it was a suicide attack and Prime Minister Vladmir Putin has been informed of the incident. Teams have been rushed to the airport.
"According to preliminary information, the explosive device was set off by a suicide bomber in the international departures hall," the Interfax news agency quoted an unnamed security source as saying.
Witnesses said, the airport building was engulfed in smoke following the explosion.
Passengers from about 2 dozen international flight including from New York, Dubai, Asghabat, Cairo, London, Vienna, Munich, Hamburg, Tokyo and Istanbul were around the area of the explosion that was not far from one of the restaurants.