Italy's Foreign Minister Antonio Tajani condemned the attack, but the commander of Camp Singara in Erbil said it had not been determined whether a missile or a drone was involved.
The base "is within a compound which includes other bases from other countries, above all Americans," Tajani told the Realpolitik television programme.
"I just spoke with the Italian ambassador to Iraq. Fortunately, all our soldiers are well and safe in the bunker."
Italy has soldiers in Erbil training Kurdistan security forces as part of an international force.
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"The type of threat is still being determined, whether it was a drone or a missile," Stefano Pizzotti, commander at Camp Singara, told the SKYTG24 news channel.
"It hit the Italian base and caused some damage to the base's infrastructure and equipment", he said.
All personnel were already in bunkers following the activation of an air threat alarm, he said.
It is not clear when the attack took place. The defence ministry did not respond to requests for further details or comment.
However, drones were shot down on Wednesday over Erbil by the US-led international forces, which are based at Erbil airport, a Kurdish security source said.
No casualties were reported, the source said.
AFP journalists reported hearing loud bangs near Erbil airport from air defences engaging drones.
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