According to the country’s official MENA news agency, another six officers were injured in the Monday accident.
The troops were part of interior ministry's Central Security Forces, which along with the army has been fighting militants behind a series of deadly attacks in the lawless peninsula near the border with Israel.
In a separate incident, a police officer and a gunman were killed in a gunfight during a foiled attempt to rob a postal vehicle carrying money in the northern Sinai town of El-Arish.
Egypt has been trying to secure its borders following the 2011 revolution, which resulted in the ouster of Dictator Hosni Mubarak.
On August 5, Sinai militants clashed with Egyptian soldiers, killing at least 16 border guards and leaving several others injured.
The outbreak of militant attacks in the Sinai region prompted the Egyptian government to deploy hundreds of troops in the restive region to prevent future violence.
Hundreds of troops have been deployed to the restive region to prevent any future attacks after President Morsi pledged to strongly respond to the "cowardly attacks," vowing that the assailants would pay for the deadly attacks.