At least 10 rockets hit Ain al-Asad airbase in Anbar province at 7.20am, coalition spokesperson Colonel Wayne Marotto said.
Speaking to The Independent from the nearby area of Al-Baghdadi, residents described hearing the base’s sirens and then at least 10 huge explosions.
They said those fleeing the area told them that several people had been wounded.
There was no immediate claim of responsibility for the attack or confirmation of casualties, but Iraqi media reported that one civilian contractor had died after having a heart attack during the barrage.
Later, the Iraqi military released a statement saying the attack had not caused significant losses and that security forces had found the launch pad used for the missiles.
Another official and local residents said that they had been found in the Al-Baghdadi area.
Wednesday’s attack comes just ahead of a three-day visit by Pope Francis, who is expected to visit six cities across Iraq, including war-ravaged Mosul to the north and Najaf in central Iraq, where he will meet the country’s top Shia cleric, Grand Ayatollah Ali al-Sistani.
Security has been tightened across the country, with Iraqi clerics saying that as many as 10,000 additional personnel will be deployed to ensure the trip goes smoothly.
Tensions have soared in recent weeks with tit-for-tat attacks between US forces and Iran-backed militias casting a long shadow on the historic papal visit.
Wednesday’s rocket attack was the first since the US struck militia targets along the Iraq-Syria border last week, in which one militiaman was killed.
The US said that its strike was in response to a spate of rocket attacks on the US presence in Iraq, including one that killed a coalition contractor from the Philippines outside Erbil airport.
The Pentagon said of the strike on the border that it was a “proportionate military response” taken after consulting coalition partners.
Col Marotto said Iraqi security forces were leading an investigation into Wednesday’s attack on Ain al-Asad.
Iraqi media reported that 10 Katyusha rockets had hit the base. Despite the security concerns, the Pope said on Wednesday he was determined to travel to Iraq because “the people cannot be let down for a second time”.
Pope Francis, who is due to arrive on Friday, asked for prayers so that the visit “can take place in the best possible way and bring about the desired fruits”. Previous plans for popes to visit Iraq have ended in failure.
The late Pope John Paul II was unable to go in 2000, when negotiations broke down with the government of the then-leader of Iraq, Saddam Hussein.