The officials, who spoke under condition of anonymity because they weren't authorized to speak to reporters, say investigations are underway Sunday and the wounded have been taken to a hospital.
Egypt has been battling an Islamic insurgency in northern Sinai for years, but attacks against the army and police increased after the July 2013 ouster of Islamist President Mohammed Morsi.
The Islamic State affiliate based in Sinai has claimed a series of large-scale assaults there.
