Police colonel Thembeka Mbele said 65-year-old Yousuf Deedat -- son of Sheikh Ahmed Deedat -- was shot in the head as he walked towards the Verulam family court on the outskirts of Durban with his wife.
Mbele said an unknown suspect opened fire, wounding Deedat in the head. He was later rushed to a hospital for medical attention, while the suspect fled in a motor vehicle in an unknown direction.
"He is in critical condition in a local hospital. While his injuries remain severe, we remain hopeful for Deedat's recovery," Deedat's family said in a statement late Wednesday.
They also requested the family's privacy be respected during the traumatic experience.
Sheikh Ahmed Deedat, who died in 2005, was a prominent South African Muslim missionary who held several interfaith public debates with evangelical Christians.
He was known across the world as a respected public speaker and writer who published several widely-distributed booklets on Islam and Christianity.
He was the founder of the Islamic Propagation Centre International, which aims for Islam to be heard and understood across the world.
His son Yousuf is a famous community activist and Muslim scholar in Durban. Police said they were still investigating the reason behind his shooting.
Source: Anadolu Agency