The Al Jazeera news channel reported that the Islamic State's local affiliate claimed responsibility.
Militants detonated an improvised explosive device and destroyed three armored vehicles.
At least 23 Egyptian soldiers were killed when suicide auto bombs tore through two military checkpoints in North Sinai in July, in one of the bloodiest assaults on security forces in years.
The assailants, whose identities were not yet known, later opened fire at survivors and commandeered a police pickup truck.
The Egyptian military and police have killed hundreds of militants and arrested a similar number of suspects as part of the country's anti-terror war.
At least 26 Egyptian soldiers were killed or wounded on July 7, 2017, in attacks on checkpoints in the Sinai Peninsula.
The officials spoke on condition of anonymity because they were not authorized to speak to the media.
At least 18 policemen, two of them officers, died in the violence, and a brigadier general lost a leg in the blast, several sources at Arish hospital said.
A statement by the Interior Ministry, which oversees security forces, said the militants were hiding in two apartments in the densely populated Ard el-Liwa neighborhood, where they held organizational meetings and planned a "series of terror attacks" in central provinces, a reference to Cairo and its twin city of Giza. One of the militants, they said, died when an explosive device he meant to use against the policemen went off prematurely, killing him instantly. The militants were said to be the suspected members of a splinter faction of the outlawed Muslim Brotherhood group.