The wounded man, 27, was apprehended when he tried to flee the scene.
The incident came six days after three people were killed and 13 were wounded in explosions in a train, a Cairo metro station and near the presidential palace.
Nine other people were reported wounded late Tuesday when a car bomb exploded in the city of Arish, in the northern Sinai peninsula.
The area has been the scene of unrest and frequent attacks against security forces since Islamist president Mohamed Mursi was overthrown in July 2013.
On Oct 24, more than 30 troops were killed in an attack in the region, which has been placed under a state of emergency and a curfew.
The Ansar Beit al-Maqdis (Supporters of Jerusalem) jihadi group Monday pledged its allegiance to the Islamic State (IS) radical group active in Syria and Iraq.
The group pledged “allegiance to the Caliph of Muslims”, referring to the leader of the IS, Abu Bakr al-Baghdadi, and promised to obey him.