The attack involved a device with the force of 7 kg TNT bomb that exploded in the international arrivals hall, which is open to people who are not passengers.
Security believes the bomb was in a suitcase brought from outside the airport, not on a plane.
Some eyewitness said that the force of the blast was such that it melt snow on the roof of the hall.
Domodedovo, which is some 40 kilometres southeast of the city centre, is the busiest airport serving Russia's capital with some 600 daily flights.
All flights from Domodedovo have been suspended, whilst incoming flights are being diverted to Moscow's Sheremetevo airport.
Today’s attack is the worst since March of last year when 40 people were killed at a Moscow metro station during morning rush hour. That attack was claimed by a Chechen group.
Sources close to the investigation said that today’s attack was the second attempt by Chechen terrorists, and is related to an explosion that destroyed a house in southeast Moscow on 31 December. The blast was caused by a bomb that blew up during its making. A woman, a probable volunteer suicide bomber, was killed. Her husband was later arrested.
President Dimitri Medvedev ordered tighter security at all of the country’s airports and train stations and delayed his departure for the World Economic Forum in Davos, Switzerland.