The suicide blast, which killed at least 35 people and injured about 150, underscores Putin's failure to put a stop to insurgency after more than a decade in power.
It prompted Medvedev to postpone his departure for the World Economic Forum in Davos, Switzerland, where he is to pitch Russia as an investment destination in the hope of attracting more cash to modernise the country's energy-reliant economy.
Medvedev vowed to find and punish those responsible, in Twitter comments less than two hours after the explosion tore through the international arrivals hall.
Police said they were stepping up security.
Those promises will ring hollow for many in a nation plagued by an Islamist insurgency in the impoverished North Caucasus. Kremlin critics say the campaign is fueled by corruption and lawlessness that also helps militants slip through the cracks of law enforcement.
The blast at Domodedovo airport came less than a year after two female suicide bombers from the North Caucasus region of Dagestan set off explosives in Moscow's subway during the morning rush hour on 29 March, killing 40 people.
It eerily echoed attacks in 2004 – days before the school hostage tragedy in the North Caucasus, Christian-majority town of Beslan – when bombers bribed their way onto two flights from Domodedovo and set off explosives, downing both planes and killing 90 people.
"The strategy to deal with the root causes of the attacks has failed so far and the security services have failed to dent the militant operations," Matthew Clements of the Eurasia department at IHS Jane's Information Group in London told Reuters.
In recent years, "the militants operating in the North Caucasus have increased the scope of operations in the North Caucasus itself and they have expanded it into 'mainland' Russia," he said.
Clements saw no direct link with parliamentary elections late this year and a 2012 presidential vote, but he said there was "a heightened risk of further attacks against high-profile targets in Russia and public areas of Moscow and other cities".
It would take more persistent mayhem to derail the ruling United Russia party, which is expected to maintain its dominance of parliament in the December vote, let alone keep Putin's chosen candidate out of the Kremlin in the March 2012 vote.
'Moscow doesn't believe in tears'
Putin, who vaulted into the presidency after leading the country into a second devastating war against rebels in Chechnya in 1999, is widely expected to return to the Kremlin in 2012 or endorse Medvedev for a second term.
But the blast could undermine public confidence in both Russian leaders, who have struggled in recent months with summer wildfires and acrid smoke that killed hundreds and unprecedented racist violence in which ultranationalists targeted minorities, mostly Muslims.
Glen Howard, president of the Washington-based Jamestown Foundation think-tank, said it would "further exacerbate the tensions created by the right-wing demonstrations in Moscow".
Financial analysts pointed out that investors in Russia, like its everyday citizens, are inured to terrorist attacks and that its markets have rebounded quickly from previous incidents.
"Moscow doesn't believe in tears," said John Winsell Davies, lead fund manager at Wermuth Asset Management – citing a Soviet movie title that has come to symbolise the hardened attitude of many Russians and investors in the country.
"I don't think any major investor will be deterred by a bomb attack from investing in any major Russian company," said Zsolt Papp of UBP Asset Management in Zurich.
"Russia is politically a stable country, remarkably stable, [...] and other factors such as the oil price play a much bigger role," he said.
But the blast is a fresh blow to Russia's image abroad, darkened in recent weeks by a new six-year prison sentence for long-jailed former oil tycoon Mikhail Khodorkovsky.
Medvedev seems unlikely to completely call off his trip to Davos, where his top economic aide said his main message would be that Russia's door is open to foreign investment.
Television footage from a smoke-choked Domodedovo in the aftermath of the blast sent a starkly different message: enter at your own risk.
Once a chaotic and dilapidated place with the grit of a Soviet train station, Domodedovo is a renovated Russian window on the world, serving scores of foreign airlines.
Germany's Lufthansa briefly halted flights to Moscow after the blast, and at least one British Airways flight to Domodedovo turned back to London.
(EurActiv with Reuters.)