The news was confirmed by US officials who several US troops were wounded in the attack.
There are also unconfirmed reports that the rocket strike killed two Iraqi soldiers.
According to the Iraqi military rockets were fired at the K1 base, where both Iraqi and American forces are based.
Speaking to CNN security sources said the Katyusha rockets were launched from a vehicle about 12 kilometres west of Kirkuk.
The vehicle, which has since been found, was located in an abandoned village.
Earlier this month five rockets narrowly missed Balad Air Base in Iraq, which hosts American forces.
Iranian backed militias have been blamed for a number of attacks on US forces in Iraq over the past few months.
ISIS cells are also believed to be based around Kirkuk although they are believed to have been greatly weakened.
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On Twitter the UK based ELINT News, which monitors global conflict, suggested pro-Iranian militias are the most likely culprit.
They commented: “How many ISIS fighters do you see driving around with MRLS [multiple rocket launchers] mounted on vehicles these days in Iranian based Iraqi forces controlled areas.
“This pretty clearly points to Iranian backed forces.
“Didn’t drive off with the vehicle to avoid being targeted in an airstrike.”
READ MORE: Rocket attacks on US targets spark fresh fears of Middle East conflict
The US Government has long accused Iranian backed groups of being behind attacks on its forces in Iraq.
In 2014 ISIS seized large parts of Iraq including its third city Mosul in a series of lightening advances.
However over the following years Iraqi forces gradually regained territory and retook full control of Mosul on July 21 2017.