About 2,500 soldiers took part in the raids on 12 villages in the city of Sheikh Zuweid, China's official Xinhua news agency reported.
The fighting was said to be ongoing, so the exact death toll was not clear.
Three vehicles said to belong to militants were destroyed.
A military official whose name was not reported said the operation "could be the biggest in Egypt's modern history," the Palestinian Ma'an News Agency reported.
Tanks, missile launchers, troop carriers and 10 helicopters were taking part in the raids.
An Egyptian security official said troops hoped to "clean all the villages in Rafah and Sheikh Zuweid area from dangerous terrorists."