The officials say the bomb struck an armored vehicle carrying soldiers to Sheikh Zuwaid near the city of el-Arish city today. The four soldiers, they said, are in a critical condition and the death toll could rise.
The officials spoke on condition of anonymity because they were not authorised to speak to the press.
Egypt has battled Islamic extremists in Sinai for years, but the insurgency has grown deadlier and spread into the mainland since the 2013 ouster of Islamist president Mohamed Morsi.