No group immediately claimed responsibility, but militants bent on toppling the Cairo government have killed hundreds of police and soldiers in the past, usually at checkpoints or police stations.
A health ministry spokesman said four Egyptians were wounded. Security sources said casualties included bazaar shop owners and police, according to Reuters.
They said three armed men tried to storm a barricade that leads to the Karnak temple site. Two men left the car and engaged in gunfire with police, who killed them. The third man in the car managed to overcome the barricade and blew himself up.
Tourism is one of the top sources of income and foreign currency earnings for the Arab world's most populous country.
Gunmen on a motorcycle shot dead two members of Egypt's tourism and antiquities police force on a road near the Giza pyramids last week.