The blast occurred Saturday in the city of Ismailia, Nile TV reported.
Egyptian military spokesman Col. Ahmed Ali said on Facebook that those who were injured in the blast suffered non-life-threatening injuries, the Los Angeles Times reported.
A second car bomb in the area was detected and disabled before it was detonated, authorities said.
This was the most recent incident in a string of attacks on government buildings in the region, CNN said. Violence in the region has been ongoing since Islamist president Mohamed Morsi was ousted from office by the Egyptian army.