Islamic State’s Egypt affiliate, Sinai Province, claimed responsibility for the attack, which it described as a suicide bombing.
The group has killed hundreds of soldiers and police since the army toppled Islamist President Mohamed Mursi in 2013 after mass protests against his rule.
Egyptian President Abdel Fattah al-Sisi has said Islamist militants pose a grave threat to Egypt, the most populous Arab country.
AFP earlier, citing state television, reported that at least three Egyptian policemen were killed in a bombing in the Sinai Peninsula.
State television said there were also wounded in the bombing in North Sinai provincial capital El-Arish.
The Islamic State group’s affiliate in Sinai said one of its militants drove an explosives-laden vehicle into a police club in the town.