Sirens blared from the embassy inside the zone, which houses government buildings and foreign missions. One security source said at least four rockets were fired and some of them landed nearby.
A military statement said that seven Katyusha rockets were fired, four that fell inside the Green Zone and three outside, which killed a child and wounded five people.
The military said earlier four rockets were fired from an eastern district of the capital, but did not provide more details.
Footage from the military showed a rocket launcher fixed on the back of a mini-truck which was set on fire.