The jihadists have also killed dozens of people in attacks targeting Egypt's Coptic Christian minority elsewhere in the country, and claimed it planted the bomb that brought down a plane carrying tourists in Sinai in 2015, killing 224 people on board.
The police suffered their injuries after a suspected militant detonated an explosive device to block them from entering the building and during an exchange of fire that followed, security sources said.
It was the deadliest attack in the northern Sinai in months.
In Monday's attack, the police convoy was travelling along the road between el-Arish and Qantara when a suspect vehicle tried to break through it, according to an interior ministry statement.
Hasm has claimed responsibility for deadly attacks on security forces during the past year.
Four additional THAAD launchers to be installed in Seongju on Thursday:MND
The four remaining launchers have been on standby at an unidentified USA base in South Korea, pending the alliance's decision. A THAAD battery normally consists of six launchers, but only two have been operational so far at the site in rural Seongju.
The officials spoke on condition of anonymity because they were not authorised to speak to the media.
The incident occurred some 30 kilometers west of Arish in northern Sinai, the heart of long-running militancy now led by the Velayat Sinai terror outfit. The suspected militants later opened fire with machine guns. According to the military, thousands of militants have been killed in the operations held against them.
An anonymous security source told Al-Ahram that three militants have been killed in the attack as well.
Monday's attack came a day after authorities said they had busted an extremist cell planning attacks in Cairo. One of the militants, they said, died when an explosive device he meant to use against the policemen went off prematurely, killing him instantly.
North Sinai has been caught in a crossfire between Egypt's security forces and militants since the ouster of the former Islamist President Mohamed Morsi.