The attack outside el-Arish also wounded five people, said the officials, speaking on condition of anonymity in line with regulations.
The bomber, they said, slowly approached the checkpoint, waited for soldiers and policemen to start searching the car before he blew himself and the vehicle up.
Islamic militants have been attacking Egyptian security forces in Sinai for years but the frequency of the attacks has dramatically stepped up since the ouster of Islamist President Mohammed Morsi in a popularly-backed July coup in what has increasingly started to resemble an insurgency in the troubled peninsula.
In northern Sinai, which has been the focal point of the attacks in the peninsula, the army and police are waging a campaign against the militants, using tanks, fighting vehicles and helicopter gunships.
The militants, some of them with al-Qaida links, are responding with suicide bombings and ambushes targeting military and police facilities, as well as their checkpoints across the northern part of Sinai, an area that borders both Gaza and Israel.
The growing violence in Sinai is coinciding with near-daily protests by Morsi supports in Cairo and across much of the city. The number of participants in these demonstrations had steadily dwindled but grew into the thousands during rallies on Oct.
The surge in the fighting in Sinai also coincides with a government campaign against Morsi's Muslim Brotherhood. At least 2,000 members of the group's members, including most of its top leaders, have been detained. Many of them are awaiting trial, including Morsi whose trial is due to begin Nov. 4. Held at an undisclosed location since his ouster, Morsi is facing charges of incitement in the murder of protesters against his rule.
At least 1,000 Morsi supporters have been killed in the crackdown by security forces since the July 3 coup.