No group has claimed responsibility for the strike but the same rockets were used in attack on Sunday night at another US base.
Four members of the Iraqi military were wounded in the eight-missile strike on Balad air base around 50 miles north of Baghdad.
The attacks come a week after Iran targeted two US bases in Iraq. No troops were hurt in those revenge strikes for America's killing of Tehran's highest ranking general Qassem Soleimani.
His assassination had been preceded by a string of attacks in recent months on US personnel in Iraq which have been attributed to the Iran-backed Kataeb Hezbollah faction of the Popular Mobilization Forces (PMF).
Seven mortar bombs fell on Sunday inside the air base and four Iraqi soldiers were wounded in the attack, two military sources told Reuters
When Soleimani was killed on January 3 he was riding out of Baghdad International Airport in a convoy with members of the PMF.
In the wake of his death the PMF has made furious calls for US troops to withdraw from Iraq and passed a resolution to that effect through the parliament in Baghdad.
Iran's limited retaliatory strikes appeared to be mainly a show of force, and deescalated tensions that still threaten to turn Iraq into a proxy battlefield.
