Etzebeth, 25, initially took over the captaincy in June when Whiteley sustained a groin injury ahead of the final Test of a three-match home series against France.
The two-time world champions start their tour of Europe against Ireland on November 11 before trips to France and Italy ahead of their concluding match against Wales on December 2.
“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,” said Springbok coach Allister Coetzee.
South Africa will also be without experienced back-rower Duane Vermeulen, who is recovering from groin surgery, as well as prop Frans Malherbe (neck), flanker Jaco Kriel and wing Ruan Combrinck (both shoulder).
Prop Coenie Oosthuizen is in line to return though after breaking his arm in the 23-23 Rugby Championship draw in Australia on September 9.
The Springbok squad for the end of year tour will be announced on October 29.