There have been no causalities reported following the strikes, which fell amid heightened tensions in the Middle East.
Two rockets dropped inside the sprawling embassy compound in Baghdad, three Iraqi security officials have claimed.
They said another hit near the coalition base, which is situated next to the embassy in the Green Zone, where government offices are based.
Colonel Myles Caggins, a spokesman for the US military operation in Iraq, said the military base had been hit by rockets just before 3.30am local time on Sunday.
He did not mention an attack on the embassy itself.
Rockets – which the US often blames on Iran-backed militias – have regularly hit the area surrounding the US embassy in Baghdad, occasionally falling inside the compound.
The attack was the latest in a recent series of strikes on Iraqi bases housing US troops.
On Thursday, a mortar shell exploded in an Iraqi military airbase in the northern Kirkuk province.
Fifty US personnel were diagnosed with traumatic brain injuries in an attack by Tehran on Ain al-Asad military airbase housing US troops in Anbar, authorities said.
The US embassy in Baghdad has also been a flashpoint amid wider US-Iran tensions in the region, which have played out inside Iraq in recent weeks.
Iraqi supporters of an Iran-backed militia stormed the embassy compound 31 December, smashing the main door and setting fire to the reception area.
Tensions have been escalating between the US and Iran since Mr Trump pulled out of a nuclear deal which aimed to curb Tehran's capabilities and reimposed crippling sanctions.
Relations were strained even further following Soleimani's death in January, with Iranian officials threatening revenge.
Additional reporting by agencies