Three people were killed and 16 injured when light aircraft dropped two bombs, officials said, hitting a parking area for planes and helicopter gunships.
The international airport - which was not damaged - was closed briefly.
Tiger rebels attacked the airport and base in 2001, killing 18 and wiping out half of the national airline fleet.
A statement from the Tamil Tiger rebel group, carried by TamilNet, claimed responsibility for the attack on the Katunayake base, which is 30km (
The group said two aircraft were used in the bombing and both planes returned to rebel-held territory safely.
"It is a measure to protect Tamil civilians from the genocidal aerial bombardments by Sri Lankan armed forces. More attacks of the same nature will follow," said the rebels' military spokesman, Rasiah Ilanthirayan.
Air force officials said no planes were hit, damage to the military facility was "minor" and that a search operation was under way.
The BBC's Roland Buerk in Colombo says the confirmation that the rebels now have an air capability confirms government suspicions that they had been smuggling in aircraft parts to be assembled in areas of the island they control.
The raid on the air force base took place at about 0045 on Monday (1915 GMT Sunday).
Flights in and out of the civilian airport were cancelled and roads cordoned off but no civilians were wounded and the runway was not damaged.
Neil Butler, a British passenger at the airport, was inside the terminal building when the attack happened.
"I heard a large thud and we all went to the window. There was a long silence and then several more explosions followed by machine gun fire," he told the BBC News website.
"The staff ran for the exit followed by the passengers. When I arrived downstairs in the check-in area a large crowd was running in a panic from the entrance where there had been more machine gun fire."
He said: "I saw what looked like kind of fireworks in the sky, like a series of red flashes. But I didn't see any aircraft going over."
The air force base, which adjoins the country's only international passenger airport, houses some of the aircraft used in recent air strikes against Tiger rebel bases in the north.
Despite a ceasefire still being in place on paper, Sri Lanka has been sliding back towards civil war, with more than 4,000 people killed in the past 15 months, our correspondent says.
The rebels have been fighting the armed forces of the predominantly Sinhalese government for much of the past 20 years.
They want to establish an independent homeland for the minority Tamils in the north and east of the country, to be called Tamil Eelam.
About 65,000 people have been killed and one million displaced by the fighting.
Güncelleme Tarihi: 20 Eylül 2018, 18:16