Etzebeth took over as skipper when Whiteley sustained a groin injury during the Test series victory over France in June.
Whiteley was expected to be fit to travel to Europe, but the number eight will not be ready in time for the Tests against Ireland, France, Italy and Wales in November and December.
Etzebeth has been an inspiration since being installed as stand-in captain and the towering lock will continue to lead his country out.
Springboks head coach Allister Coetzee said: "Eben has really taken to his role as captain of the Springboks and it makes sense to retain him. I know he is well respected by talking to opposition coaches and referees, and he enjoys the respect of his peers.
"With Eben at the helm for the Castle Lager Outgoing Tour, we are looking forward to continue our process of building continuity, cohesion and experience within this team as we also start to build towards the 2019 Rugby World Cup in Japan."
Prop Coenie Oosthuizen (fractured arm) and loose forward Uzair Cassiem (rib) will be available to tour, but number eight Duane Vermeulen will not be in the squad after undergoing a groin operation.
Flanker Jaco Kriel (shoulder) and Frans Malherbe (neck) are also unavailable.
Photo by Getty Images. Caption: South Africa's stand-in captain Eben Etzebeth