Abdallah Mursi, 24, began to feel spasms while driving in Cairo with a friend and died shortly afterward, his brother Ahmed said.
Their father was the first democratically elected head of state in Egypt's modern history. He died in June from a heart attack at age 67 after collapsing in a Cairo court while on trial on espionage charges.
A top figure in the now-banned Muslim Brotherhood, Mohamed Mursi had been in jail since being toppled by the military in 2013 after barely a year in power, following mass protests against his rule.