Security has been ramped up across the Russian capital, with its other airports and transport hubs on high alert.
Pavel Tokarchuk, director of Russian Ministries' Moscow office, described the mood across the city as "panicked".
He asked for prayers in a message to supporters on the ministry's website.
He wrote: "I was there [at Domodedovo] a week ago flying through to Siberia on a Project Hope trip. Very crowded airport [sic]. What has happened is just unbearable.
"Please, raise your prayers for the relatives of the victims, and for the more than 50 people who are in the critical conditions because of their injuries."
No one has come forward to claim the attack, although Russian news agencies report that investigations are currently focused on three men from the North Caucasus.
It is the third deadly terrorist attack in Russia in less than two years. Last March, two female suicide attackers killed 40 people when they detonated bombs in Moscow's metro system. In November 2009, an attack on a train between Moscow and St Petersburg left 26 people dead.
British Foreign Secretary William Hague said he was deeply "shocked and saddened" by today's attack.
"On behalf of the UK, I send condolences to all those who have lost relatives or been injured," he said.
"British officials are in urgent contact with the Russian authorities to establish the facts and to provide consular support to any British nationals who may have been affected."
US President Barack Obama described the attack as "outrageous".