Nartey, coached by Juergen Klinger at the University of Bath Sports Training Village, needed just 28 seconds to beat Tunisia’s Hamza Barhoumi by ippon in the fight for third place in the under-73kg category.
The London 2012 Olympian had also started the competition with a quick-fire Pool C victory, against Gabon’s Pierre Ginvard Mavoungou, but missed out on a place in the semi-finals following an ippon defeat to Gambia’s Faye Njie.
That put Nartey into the repechage and he overcame Tunisia’s Bassem Mtiri after a tough battle before beating Barhoumi to secure a podium place.
The All-Africa Games, which conclude on Saturday, feature 54 countries and 22 sports. This year’s edition marks the 50th anniversary of the continental competition.