Later, Reuters reported at least three shells that hit the centre of Baghdad, with one of them falling about 100 metres away from the US embassy. The projectiles were reportedly identified as Soviet-made Katyusha MLRS rockets.
Videos with sirens ringing out have emerged on social media.
Tensions have recently escalated in the region, with Iraq caught in the middle of the clashes.
On Friday, Iran's top military commander Qassem Soleimani was killed in the US targeted attack on the Baghdadi International Airport. Iran took its "revenge" by conducting airstrikes on US military bases in Iraq on Wednesday.