Islamic State claimed responsibility for the attacks on several websites.
Several explosive devices were planted on the road in Rafah and southern Sheikh Zuwayed and were remotely detonated as soon as the vehicles passed by, the sources said.
Egypt’s military spokesman could not immediately be reached for comment.
Egypt is battling an insurgency that gained pace after its military overthrew President Mohamed Mursi of the Muslim Brotherhood, Egypt’s oldest Islamist movement, in mid-2013 following mass protests against his rule.
The insurgency, mounted by Islamic State’s Egyptian branch, Sinai Province, has killed hundreds of soldiers and police and started to attack Western targets within the country.
President Abdel Fattah al-Sisi, the former military chief who led Mursi’s ouster, describes Islamist militancy as an existential threat to Egypt, an ally of the United States.
Islamic State controls large parts of Iraq and Syria and has a presence in Libya, which borders Egypt.