The incident took place on Sunday evening, the official told Xinhua news agency, adding: "One of the rounds landed at the bank of Tigris River close to the US embassy."
The heavily fortified Green Zone has been frequently targeted by mortar and rocket attacks. The roughly 10 sq.km zone is located on the west bank of the Tigris River, which bisects the Iraqi capital.
On Saturday night, Abu Ali al-Askari, security leader of the Shia militia Kata'ib Hezbollah (KH) warned the Iraqi security forces to move away from the US bases with no less than 1,000 metres starting from Sunday.
"The leaders of the security services must abide by the safety rules of their fighters and not allow them to be a human shield," al-Askari said.
The latest attack came after the January 3 US drone attack ordered by President Donald Trump killed Qasem Soleimani, commander of the Quds Force of Iran's Islamic Revolution Guards Corps, and Abu Mahdi al-Muhandis, deputy chief of Iraq's paramilitary Hashd Shaabi forces.
The attack took place on the Baghdad international airport's road.
Iran's Supreme Leader Ayatollah Ali Khamenei and President Hassan Rouhani have vowed to retaliate against the US over Soleimani's death.
The January 3 attack also came after Iraqi protesters on Tuesday stormed the US embassy compound in Baghdad to protest the American airstrikes conducted on December 29 against five bases of Iran-backed militias in Iraq and Syria, claiming the lives of 25 militants.
( With inputs from IANS )