The Ethiopian attack, the first on Asmara in the two-week offensive, comes as Ethiopia and Eritrea resume peace talks on Monday in an effort to end the two-year war between the two countries.
Four Ethiopian MiG fighters swept in over Asmara's international airport, bombing and firing rockets at a military airstrip next to it.
Smoke rose into the air and ambulances rushed to the military airfield, which lies next to the capital's civilian airport and a housing estate.
Two Eritrean MiG fighter planes were dispatched in pursuit.
Two of the bombs landed on the airport access road and a building in the military complex was hit, but there has been no mention of any military casualties.
The two sides are not expected to meet face-to-face at the talks in Algeria's capital, Algiers, but officials of the Organisation of African Unity (OAU) will mediate at the negotiations.
The attack is a clear message at the start of the talks that Ethiopia is determined to make the most of its military ascendency.
An Eritrean government official has condemned the attack saying civilians had been put at risk.
"You don't bomb in Asmara without hitting areas where there are civilians," he said.
The Eritreans say two civilians were taken to hospital, but their condition is not known.
Clashes
Reports said clashes had intensified on Monday near the towns of Tsorena and Adi Keyah, 80 km south of Asmara, and at Bure, further east, from which the Eritreans had earlier said they would withdraw.
There have been reports of thousands of Eritrean civilians fleeing the combat zone.
A peace plan drawn up by the OAU calls on the Eritrean army to withdraw to the positions it held before the war broke out in 1998.
The international community has called on Ethiopia - which now occupies substantial areas of indisputable Eritrean territory - to do the same.
Eritrea has said it will withdraw, in line with an OAU peace plan.
Ethiopia declared victory in the border war on Thursday but it says it will negotiate and continue fighting at the same time.
It says it will not withdraw until it is satisfied that Eritrea has pulled back from its territory but insists that its troops have no intention of permanently occupying parts of Eritrea.
Refugees
In southern Eritrea, thousands of new refugees have left their homes, as Ethiopian troops continue to push beyond the disputed border region.
The grounds of a secondary school in Dubarwa have been turned into a temporary camp, to which refugees have been taken in lorries supplied by the Eritrean authorities.
Hundreds of thousands of people have already been displaced since fighting resumed just over two weeks ago.
The celebrations were intended both to mark what the Ethiopians see as a military victory in the war against Eritrea, and the ninth anniversary of the toppling of the Dergue regime led by Mengistu Haile Mariam.
