The interior ministry, on its Facebook page, said three gunmen in a car without license plates fired at the checkpoint in Sadat City, an industrial zone 100 kilometres (60 miles) from the capital.
Two civilians were among the five wounded, the health ministry said.
It was not immediatly clear if the attack was carried out for criminal motives or by jihadists, who have mounted a string of deadly operations against security forces since the military ousted Egypt's Islamist president Mohamed Morsi in July 2013.