Aid agencies have warned of the civilian cost of fighting
It was not clear how many times the airport was struck but at least one person was reported injured.
Mogadishu is held by an Islamist militia, which has been fighting the Ethiopia-backed interim government.
Ethiopia's prime minister has said his country is "at war" with the Islamists, and the Red Cross has urged all parties to protect civilians from harm.
Thousands of Somalis have fled the escalating violence, and the Red Cross says the fighting is straining an already weak support system in the country.
The airport in Mogadishu was recently reopened by the Union of Islamic Courts (UIC) - which holds most of central and southern Somalia.
The BBC's Adam Mynott, in the region, says the attack is a clear indication that Ethiopia is carrying through its threat to hit Islamist positions in pursuit of what it claims is self-defence.
A spokesman for the UIC, Abdirahman Janaqow, told the Associated Press that the Islamists would stand firm against Ethiopia.
As Ethiopia struck Mogadishu airport, Somalian and Ethiopian troops forced Islamist forces to withdraw from one flashpoint close to the border.
Troops captured a checkpoint outside the town of Beledweyne and UIC forces then left the town, the scene of sustained fighting on Sunday.
There were also reports of heavy fighting at the central flashpoint of Burhakaba, close to the seat of Somalia's transitional government in Baidoa.
Somali government forces have been fighting the UIC for six days now, initially around Baidoa but later along a 400km (250 mile) front line.
On Sunday Ethiopia admitted for the first time its troops were fighting in Somalia and began attacking the UIC on four fronts.
Ethiopian Prime Minister
"We are not trying to set up a government for Somalia, nor do we have an intention to meddle in Somalia internal affairs. We have only been forced by the circumstances," Mr Meles said.
"We want to end this war urgently and we hope that Ethiopian people stand by the defence forces."
The UIC, which has seized control of much of southern and central Somalia, says Ethiopian troops have been fighting alongside government forces for months.
The Islamist group - which controls most of the south, including the capital, Mogadishu - on Saturday appealed for foreign fighters to join its troops in a "holy war" against Ethiopia.
The UN estimates that at least 8,000 Ethiopian troops may be in the country, while rival Eritrea is said to have deployed some 2,000 troops in support of the Islamic group.BBC News