Five militants were also killed in the ensuing exchange of fire, while others escaped and were being pursued security forces, according to a statement.
The attack took place west of the city of El-Arish, as local people celebrated the Islamic festival of Eid al-Fitr.
The jihadist group Islamic State (IS) later said it was behind the attack.
A claim published by its Amaq news agency said militants killed 10 police officers in two simultaneous attacks on checkpoints near El-Arish.
Egyptian state media meanwhile broadcast photographs purportedly showing the bodies of several of the attackers.
An IS affiliate called Sinai Province has killed hundreds of security personnel in attacks since the military overthrew Islamist President Mohammed Morsi in 2013.
In February 2018, three months after gunmen killed more than 300 worshippers at a Sinai mosque, the military launched a major campaign “to clear Egypt’s territory of terrorist elements”.
Since then, the authorities have announced the deaths of some 650 militants and 50 soldiers, according to an unofficial tally by AFP news agency.
A report by the US-based group alleged that the security forces were making arbitrary mass arrests, using torture, carrying out extrajudicial killings, and possibly launching air and ground attacks against civilians.
HRW said IS militants in the peninsula were also guilty of horrific crimes, including kidnapping and torturing civilians and summarily killing captured security forces.
The government dismissed the report on Tuesday, saying it was “full of lies and fabrications about the situation in Sinai”.
The military has effectively banned independent reporting from the peninsula and has imprisoned journalists who have covered events there, according to HRW.