Col. Ahmed Mohammed Ali said Mohammed Hussein Muhareb and his son were killed after troops closed in on his motorcade and a firefight ensued.
He said Muhareb was wanted for taking part in various attacks against troops in the region.
Another militant on a motorcycle was also killed, Ali said, while one officer was wounded and four militants were arrested.
Two military officials in Sinai said some militants fled in another car after the fighting, in an area between al-Joura and al-Muqatta village, south of the town of Sheikh Zuweid. They said the troops were acting on a tip.
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In the latest of a stepped-up campaign of attacks against troops, a suicide car bomb hit a bus convoy of off-duty Egyptian soldiers last week in the Sinai Peninsula, killing 11 soldiers and wounding 37.
The northern Sinai region, which borders the Gaza Strip and Israel, has been restless for years.
Extremist militants operate in disparate groups there and are believed to have grown in numbers since the political upheaval following the 2011 ouster of Hosni Mubarak, largely due to a negligible police presence in the area.
This summer, government troops intensified their raids in towns and villages there, killing and arresting a number of suspects.
Military chief Gen. Abdel-Fattah el-Sissi said yesterday there is no more tolerance for attacks on his troops.
"No more mercy or hesitation for those who raise arms against the military," he told a group of officers in televised comments.
Muhareb is widely respected among the various militant groups in Sinai, and was a leading figure in a radical group known as Takfir wil-Hijra.