The incident took place on Friday night in the city of el-Arish, North Sinai's provincial capital, Egyptian media reported.
The IED was supposed to explode when security forces were passing, but it was detonated when civilians were present at the site.
No individual or militant group has yet claimed responsibility for the blast, but such incidents are often blamed on militants affiliated with the Daesh group.
The bombing came one day after the Egyptian military said it had killed Abu Duaa al-Ansari, the leader of the Sinai branch of Daesh.
Ansari was killed in airstrikes targeting the militants' strongholds near Arish along with over 45 of his aides.
The air raids further destroyed a number of weapon and ammunition stores as well as explosives belonging to the extremists.
Egyptian Brigadier General Mohammed Samir said on his Facebook page that Ansari was killed in an operation guided by "accurate intelligence."
The government in Cairo views Sinai Peninsula as a safe haven for hardliner militants.
The sparsely populated desert region has been under a state of emergency since October 2014, following a deadly attack that left 33 Egyptian soldiers dead.
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 affiliated with Daesh have claimed responsibility for most of the Sinia assaults, mainly targeting the army and police.
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