According to security sources, two cars drove up to a security checkpoint in a residential area whereupon two people opened fire.
One of the attackers is said to have been killed by the police.
The attack is considered an act of terrorism, the first in Egypt outside the Sinai Peninsula in nearly three years.
Egyptian security forces have been trying for years to quell the jihadist insurgency in northern Sinai, which has escalated since the 2013 ouster of President Mohammad Mursi, of the Muslim Brotherhood.
Scores of police, military and suspected jihadists have since been killed as a result of the insurgency.
In May, at least 16 Egyptian soldiers were killed in two attacks.