Reports indicated that rockets had landed near the Baghdad Diplomatic Support Centre (BDSC), which is located in the Baghdad International Airport. The rockets are said to have hit the tarmac but did not cause any casualties.
The BDSC is a diplomatic location and part of the US Embassy, hosting American diplomatic personnel and troops.
Initial reports had suggested that up to four Katyusha rockets were launched towards Camp Victory, and that a fire reportedly broke out on the base due to the strike.
Videos have emerged on social media appearing to capture the moment the base was targeted.
The base itself is approximately five miles from the Baghdad International Airport. It has not been reported who is responsible for the attack.
Camp Victory was the lead base for US military operations during the Iraq war, before being handed over to the Iraqi government in 2011.
The attack comes near the anniversary of a US drone strike at the Baghdad International Airport that killed Iranian General Qasem Soleimani. The strike also killed Abu Mahdi al-Muhandis, a deputy commander of Iraq's Popular Mobilisation Forces.
US forces had been warned that an uptick in attacks might occur over this period.
On Monday, two armed drones were shot down at Baghdad International Airport, on the anniversary of Iranian General Qasem Soleimani's assassination. There were no reported damages or injuries from the incident.
According to sources, one of the wings of the suicide drones from Monday's attack had "Soleimani's revenge" painted on it. No group immediately claimed responsibility for the attack.
US-coalition forces had carried out strikes against targets in Syria on Tuesday. It is unknown if the rocket fire in Baghdad is related.