Ammar Badie, a 38-year-old computer engineer, died of a bullet wound in Ramses Square in Cairo during protests yesterday, the party said on its Facebook page.
Nearly 100 people were killed in clashes between security forces and protesters across Egypt yesterday. Hundreds of supporters of ousted President Mohammed Morsi were still holed up in the al-Fateh mosque in Cairo's Ramses Square, which witnessed fierce street battles.
Ammar's father Badie, the Brotherhood's spiritual leader, was arrested after the ouster of Morsi and charged with inciting violence. His current whereabouts are not known.
Khaled Fernas Abdel-Basit, 30, was killed during protests in Ramses Square, his relative Ahmed Seif al-Islam was quoted as saying by the agency.
The Brotherhood has been protesting across the country since the army deposed Morsi on July 3. The group's leaders today called for a week of protests after the death 95 people in yesterday's clashes.
Meanwhile, the Sky network reported that unknown persons broke into Badie's home south of Cairo and torched it.