The blast occurred around 4:30 p.m. at the entrance of the international arrivals section. Authorities were still trying to tally the exact number of people injured in the blast.
The Russian Ministry of Emergency Situations said that there were 110 wounded people still in hospitals.
On Monday, the Russian National Anti-Terrorist Committee had said 35 people died and 152 were wounded in the explosion.
Domodedovo is 22 kilometers (14 miles) southeast of Moscow. According to the airport's website, it is the largest of Moscow's three airports, as well as the busiest in terms of passenger traffic.
It was still not immediately clear who was responsible for Monday's blast, though previous terror attacks in Russia have been blamed on militants from the North Caucasus region.
Over the course of the last decade, bombers have hit trains and planes operating in and traveling out of Moscow at least four times, with a combined death toll more than 100 victims. In 2004, two planes blew up nearly simultaneously, after taking off from Domodedovo airport.
That attack was linked to Chechen suicide bombers.
An explosive device derailed an express train in November 2009, killing at least 26 people. Chechen rebels were blamed again.
Medvedev had strong words for the perpetrators of the attack.
"We must do everything in order for the criminals who committed this crime to be established, found and brought to justice. And the nest where these bandits are hiding, whatever their name is, should be exterminated," Medvedev said.
CNN's Maxim Tkachenko contributed to this report.
