Ashour Shwayel, who served as interior minister in the government of former prime minister Ali Zeidan, and his son were seriously hurt in the blast, said the spokeswoman of Al-Jala hospital, Fadia al-Barghati.
A security source said the blast was caused by an explosive device placed inside a car parked near Abu Houraira mosque in the central Al-Majouri neighbourhood of the eastern coastal city.
Benghazi was the cradle of the 2011 revolution that toppled and killed veteran dictator Moamer Kadhafi.
The GNA is opposed by a rival administration that is based in Libya's far east and backed by military strongman Marshal Khalifa Haftar, whose forces are battling jihadists in Benghazi.