Three Katyusha rockets fell on Baghdad International Airport, the military-run Security Media Cell said in a statement early on Friday.
The rockets landed near the air cargo terminal, burning two vehicles and injuring several people, Security Media Cell said.
At least one person was killed and 9 others wounded, police and medical sources said.
There was no immediate claim of responsibility.
Supporters of Iranian-backed Iraqi paramilitary groups stormed the U.S. Embassy in Baghdad on Tuesday following U.S. air raids on Sunday against Kataeb Hezbollah militia bases in retaliation for missile attacks that killed a U.S. contractor in northern Iraq last week.
Tension between the United States and Iran has ramped up in the region over U.S. economic sanctions hurting the Iranian economy. The two sides have traded blame over attacks on oil installations, militia arms depots as well as military bases hosting U.S. forces.