The attack took place as Muslims in the city of el-Arish were holding prayers marking the holiday of Eid al-Fitr, which follows the holy month of Ramadan, early in the morning.
Two officers and eight conscripts were among those killed, according to the officials, who spoke on condition of anonymity because they were not authorized to talk to reporters.
The Islamic State group, through its Amaq news agency, claimed responsibility for the attack.
The officials said the militants attacked the checkpoint south of el-Arish and seized an armored vehicle to make their getaway, but a warplane chased them down in the desert, killing at least five.
The Interior Ministry later released a statement saying eight police were killed in the attack. The discrepancy between the casualty figures could not immediately be resolved.
Egypt has battled Islamic militants for years in the Sinai Peninsula in an insurgency that has occasionally spilled over to the mainland, striking minority Christians and occasionally tourists.
The insurgency grew deadlier and militant attacks more frequent after the military's 2013 ouster of an elected but divisive Islamist president, Mohammed Morsi.
In Egypt, an all-out campaign by the military since early 2018 has mainly halted high-profile attacks by IS and other militants.