At least two civilians were also wounded and the rockets damaged cars and other property, security officials said, without providing more details.
The identity of the attackers was not immediately clear, and American forces are often targeted by forces including ISIS, but American officials including former Secretary of State Mike Pompeo have blamed Iran-backed groups for previous strikes on U.S. forces in recent years.
This is thought to be the first missile attack on a Western target in Iraq since US President Joe Biden took office last month.
Biden's administration is weighing a return to the Iran nuclear deal, which his predecessor Donald Trump abandoned in 2018, that aimed to curb Iran's nuclear programme.
Tension between the United States and Iran sent the Middle East to the edge of a full-scale confrontation in January 2020 after a USA drone strike killed Iranian military mastermind Qassem Soleimani in Baghdad.
Five other civilian contractors were also wounded, Army Col. Wayne Marotto, a military spokesman for the US -led coalition, said in a statement on Twitter, citing initial reports.
Former Iraqi prime minister and senior Kurdish official Hoshyar Zebari said "five Katyusha rockets" hit the city of Erbil and some diplomatic facilities and residential areas. Reuters reporters heard several loud explosions and saw a fire break out near the airport.
Asaib Ahl al-Haq threatened to fight Turkish troops if their operations expanded and another pro-Iran faction, Ashab Ahl al-Kahf, claimed on Monday it had attacked a Turkish military base along the Iraqi border. One U.S. service member was wounded, he said.
A little-known group known as Awliya al Dam (Guardian of the Blood) brigades claimed responsibility for the attack, saying it had launched the rockets in revenge for the deaths of "the martyred leaders". It provided no evidence for its claim.
The United State condemned the attack.
In a statement, the Kurdistan region's interior ministry confirmed "several rockets" had hit the city and said security agencies had launched a "detailed investigation", urging civilians to stay home until further notice.
Groups that some Iraqi officials say have links with Iran have claimed a series of rocket and roadside bomb attacks against coalition forces, contractors working for the coalition and USA installations - including the embassy in Baghdad - in recent months.