Two policemen were killed early on Tuesday at the Upper Egypt governorate of Qena, the state Nile News channel has reported.
A security source was quoted as saying that the policemen were among a patrol that spotted suspected members of a gang known for committing robberies in Naga Hammadi.
The suspects tried to escape and the patrol gave chase, with both exchanging fire. Two policemen were killed in the shootout and one gang member was injured before being arrested.
The suspects also seized one of the police force's patrol vehicles. Police are still looking for the other suspects.
The shootout is the second one in less than a month. Earlier, a policeman was killed in Minya while intervening in a clash between two families.
The trade in unlicensed weapons has been a growing phenomenon in the Upper Egypt area, particularly after the 2011 revolution which toppled former President Hosni Mubarak.