Three of the dead were Iraqi soldiers and two were policemen, the military statement said, adding that 11 Iraqi fighters were also wounded, some of them critically.
The civilian was a cook working at an unfinished airport outside the holy shrine city of Karbala, where another civilian was also wounded in the raids.
The airport's media head Ghazwan Issawi confirmed the cook's death to AFP and said the airport had also suffered material damage.
"Five missiles hit the administrative building at the airport and 18 cars were destroyed," Issawi told AFP.
"We are waiting for security forces to come and begin their investigation," he said.
The volley of strikes, which began around 1:00 am (2200 GMT Thursday), hit five weapons storage facilities belonging to the Hashed al-Shaabi military network, according to the Pentagon.
It was in response to a rocket attack on an Iraqi base late Wednesday that killed two US military personnel and one British soldier, and which the US blamed on hardline Hashed factions.
The attack was the 22nd since October on US interests in Iraq -- but by far the deadliest.
US diplomatic offices have come under attack as well as the bases where the 5,200 American troops in Iraq are stationed.
The Iraqi government was quick to condemn the rocket attack but civilian officials had yet to comment on the retaliatory US strikes more than 12 hours after they took place.
The military said the US attack was a violation of Iraq's sovereignty that would only lead to more instability in a country already squeezed by spiralling tensions between its two main allies, Washington and Tehran.
"It leads to escalation and deterioration of the security situation in the country and exposes everyone to more risks and threats," it said.
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