Iraqi officials said dozens of people were injured in the attack on the fortified zone, where the U.S. Embassy and several Iraqi government and military offices are located, Iranian government-backed Press TV reported.
Witnesses told CNN rockets, or possibly mortars, caused explosions on a road between the Foreign Ministry and one of the main checkpoints into the Green Zone.
Iraq Prime Minister Nouri al-Maliki and other officials were attending the parade. The event marked the first time Iraq noted the founding of the country's army since the 2003 U.S.-led invasion, CNN said.
The attack came one day after multiple explosions in southern Iraq and Baghdad killed at least 78 people.