The attack follows a rocket strike the previous evening that targeted an Iraqi military base inside the Baghdad airport complex, which also houses a support centre for the US embassy.

Iraq has been drawn into the broader Middle East war that started on February 28 despite seeking to avoid it at all costs. Pro-Iran armed groups have claimed responsibility for attacks on US interests in Iraq and across the region, while strikes have also targeted the groups.

"A civilian was injured in the al-Shaljiya area of Baghdad when shrapnel from an air defence system intercepting a drone fell," the police source said.

The neighbourhood is near Baghdad's Green Zone, which hosts embassies and government offices.

The night before, a rocket strike on an air base from the outskirts of the capital destroyed an Iraqi Antonov-132 aircraft but caused no casualties, the ministry of defence said.

The base is near a US diplomatic and logistics hub inside the Baghdad airport complex, which has been repeatedly targeted since the start of the war.

A military official told AFP that "rockets fell inside the diplomatic support centre early Monday morning, causing a fire".

Earlier this month a security official told AFP that the US diplomatic hub had evacuated much of its personnel.

Since the outbreak of war, pro-Iran factions under the umbrella of the Islamic Resistance of Iraq -- which have repeatedly claimed attacks against US interests -- have also been targeted by strikes they blame on the US or Israel.

Late Monday, the coalition condemned the use of rockets in the city.

The incidents come after Washington and Baghdad said last week they would "intensify cooperation" to prevent attacks and ensure Iraqi territory was not used to launch assaults against US facilities.

Two drones targeted the US embassy over the weekend, though neither hit their target.

The influential pro-Iran armed group Kataeb Hezbollah said on March 19 it would pause attacks on the diplomatic outpost for five days, twice extending the pause.