One of two men aboard the motorcycle was wounded and detained and the second was apprehended by police after a pursuit. No police or civilians were reported hurt.
In June, suicide bombers suspected of belonging to Daesh killed 41 people and wounded some 240 others with gunfire and explosives at the airport.
The latest incident did not affect flights at Ataturk, Europe's third-busiest airport, Reuters reported. Ataturk is the hub of state-run carrier Turkish Airlines.
It was not immediately clear why the police ordered the men to stop.
On Friday, a car bomb detonated in the mainly Kurdish city of Diyarbakir, killing 11 people and wounding at least 100. Officials blamed the autonomy-seeking Kurdistan Workers Party (PKK), although Daesh claimed responsibility for the attack, according to the group's Amaq news agency.
Kurdish militants, Daesh radicals and far leftists have all staged attacks on civilians in Turkey in recent years.