Elgar will replace veteran Kallis, who has been given rest ahead of the ICC World Twenty20 in September, reports said.
Right-arm spinner Imran Tahir was included as lead spinner, along with Ryan McLaren playing the role of an additional seamer.
“Dean has been in our plans for some time and might well have made his debut last year but for injury,” said Andrew Hudson, CSA selection convener.
“Imran is a genuine wicket-taking bowler and his selection enables us to explore our options in this area.
“Ryan has just come off some exceptional form for the South Africa A side and the added depth he provides in the seam bowling department will allow us to rotate players if we feel the need arises,” he said.
AB de Villiers (c&wk), Hashim Amla, JP Duminy, Faf du Plessis, Dean Elgar, Imran Tahir, Ryan McLaren, Albie Morkel, Morne Morkel, Justin Ontong, Wayne Parnell, Robin Peterson, Graeme Smith, Dale Steyn, Lonwabo Tsotsobe.