Most American soldiers stationed at the Balad base had already left amid soaring tensions between Washington and Tehran. Iraq's military said four local soldiers were wounded in the attack.
At least six mortar shells fell inside the Balad air base north of Baghdad on Sunday, wounding four Iraqi soldiers, Iraq's military said.
The base, which lies about 80 kilometers (50 miles) north of the capital, also houses US troops, but most of the Americans stationed there had already been pulled out amid rising tensions in the region between the US and Iran.
"There are American experts, trainers and advisers at the base,'' said one Iraqi defense official. Defense officials would only speak to the press on condition of anonymity.
US Secretary of State Mike Pompeo said he was "outraged" by reports of the attack.
"These continued violations of Iraq's sovereignty by groups not loyal to the Iraqi government must end," he added in a second tweet.
A statement from the Iraqi military said eight Katyusha rockets had been fired at the Balad base in Sunday's strike, hitting the runway and gate. There has been no claim of responsibility for the attack.
One air force officer and three enlisted men, all Iraqis, were wounded, but none were killed.
Second missile attack in Iraq
Tehran launched missile attacks on American targets in Iraq earlier this week in response to the US killing of Iranian General Qassem Soleimani in Baghdad on January 3.
A Ukrainian passenger plane was also accidentally targeted by Iranian missiles, killing 176 people.
A military source cited by the AFP news agency said "there are no more than 15 US soldiers and a single plane at [Balad]," because the majority of US advisers and other personnel had been evacuated.