An adult also was killed in the attack on a street filled with children going to school, the BBC said. The boys' father, Baha Balousheh, led a crackdown on Hamas 10 years ago.
The attack came a day after gunmen fired at Interior Minister Saeed Seyam's convoy in Gaza. Seyam, a senior Hamas leader, was not harmed.
Monday's attack in Gaza took place as children arrived at several schools in the city's Rimal district, police said. Gunmen fired more than 70 bullets at the vehicle carrying Balousheh's children, ages 6 to 10, police said. At least two other children were injured.
Hamas spokesman Fawzi Barhoum condemned the shooting as an "awful, ugly crime against innocent children."