The officials, who spoke on condition of anonymity because they weren't authorized to speak to reporters, said the explosion took place Monday morning in the Taweel al-Amir area south of Rafah and that the injured were taken to the military hospital in Al-Arish.
Egypt has been battling insurgency in northern Sinai for years, but attacks against the army and police increased after the July 2013 ouster of President Mohammad Mursi.
The ISIL affiliate based in Sinai has claimed a series of large-scale assaults there.