The attack came as Iran and its allies in Iraq marked the second anniversary of the assassination of top Iranian general Qassem Soleimani.
Soleimani was killed in a drone strike near Baghdad airport ordered by then-US president Donald Trump.
Commenting on the attack, an official of theUS-led international military coalition said the base's defence system had engaged "two fixed-wing suicide drones. They were shot down without incident".
"This was a dangerous attack on a civilian airport," the coalition official said in a brief statement.
There was no immediate claim of responsibility for the attack. Armed groups that some Iraqi officials say are backed by Iran have claimed responsibility for similar incidents in the past.
Footage provided by the coalition official showed what the official said was debris of two fixed-wing drones destroyed in the attack, with writing clearly visible on the wing of one drone reading "Soleimani's revenge".
Soleimani, head of an elite overseas unit of Iran’s Revolutionary Guards, was killed along with Iraqi militia leader Abu Mahdi al-Muhandis on Jan 3, 2020, in a US drone strike on his convoy at Baghdad airport.
Hundreds of supporters of Iran-backed militia groups gathered on Sunday at Baghdad airport to mark the anniversary of Soleimani's death and to chant anti-American slogans.