Officials said it was a homemade bomb. No one has claimed responsibility for the blast.
President Dmitry Medvedev immediately ordered authorities to beef up security at Moscow's two other commercial airports and other key transport facilities. He also canceled plans to fly out Tuesday to Davos, Switzerland, where he aimed to promote Russia as a profitable investment haven to world business leaders.
Medvedev told officials, "From the preliminary information we have, it was a terror attack."
"I saw the suitcase, the suitcase was on fire, and I saw the man from behind," said eyewitness Artyom Zhilinkov. "Either the man blew up something, or something went off on the man's body, or the suitcase went off."
Among the victims were celebrated Ukrainian playwright Anna Mishutina.
Hours later, with cleanup crews still continuing their work, travelers once again boarded flights shaken, but undeterred.
At Los Angeles International Airport late Monday afternoon, flights to Moscow were still on schedule. However, they were not landing at the airport that was the target of the deadly blast.
In Washington, President Barack Obama condemned the "outrageous act of terrorism" in Moscow. Obama also extended his condolences to the Russian people, whom he says have suffered greatly from terrorism.
White House press secretary Robert Gibbs said the U.S. will extend any assistance the Russians may want.
Chechen militants have claimed responsibility for previous terror attacks in Moscow, including a double suicide bombing on the subway in March 2010 that killed 40 people and wounded more than 100.
Some are now raising concerns about safety at Russia's airports. The country is hosting the 2012 Winter Olympics and the World Cup in 2018.
The Associated Press contributed to this story.