According to a statement released by the ministry, the incident took place on Tuesday when "unknown" assailants fired a rocket-propelled grenade at the police patrol on a road leading to the town of Sheikh Zuweid, located in North Sinai Province.
The attack killed three riot policemen and injured eight others, the statement said.
No individual or militant group has yet claimed responsibility for the assault, but it bears the hallmark of militants affiliated with the Takfiri Daesh terrorist group.
Sinai Peninsula has been under a state of emergency since October 2014, following a deadly terrorist raid that claimed the lives of 33 Egyptian soldiers.
Over the past years, militants have been carrying out anti-government activities and fatal attacks, taking advantage of the turmoil caused in Egypt after democratically-elected President Mohamed Morsi was ousted by the military in July 2013.
Militants from the Takfiri Velayat Sinai group, previously known as Ansar Bait al-Maqdis, have claimed responsibility for most of the attacks, mainly targeting the army and police. In November 2014, the group pledged allegiance to Daesh, which is mainly wreaking havoc in Iraq and Syria.
The government in Cairo views the volatile Sinai Peninsula as a safe haven for terrorists.