Allrounders Chris Morris and Andile Phehlukwayo, and fast bowler Duanne Olivier were the players to miss out on selection, after having been part of the squad for the Tests against India.
Faf du Plessis, Quinton de Kock, AB de Villiers and Temba Bavuma, all of whom missed all or part of the ODI and T20I series against India due to injuries, were named in the Test squad. Dale Steyn, who was injured during the first Test against India, was not.
Klaasen travelled as South Africa's back-up Test wicketkeeper on the tour to New Zealand last March but did not play a game. He's scored 292 runs at 48.66 for Titans in the 2017-18 Sunfoil Series, South Africa's first-class competition, and played match-winning innings in the Johannesburg ODI and Centurion T20I against India.
"Klaasen has been tremendously impressive in the white-ball matches he has played for the Proteas and we firmly believe he can become just as good a player in the five-day format," CSA National Selection Panel convener Linda Zondi said. "He has averaged nearly 50 with the bat in Sunfoil four-day cricket this season and hit two centuries. We are also keen to have a back-up wicketkeeper to de Kock in the squad."
Mulder, 20, was a non-playing member of the Test squad against Bangladesh at the start of the summer in late September. Ottis Gibson, who attended a round of first-class matches soon after his appointment as South Africa coach, had been impressed with Mulder and identified him as a future prospect.
Mulder averages 61.66 for Lions in the 2017-18 Sunfoil Series - 370 runs in nine innings - and has played one ODI for South Africa, against Bangladesh in October last year.
"The selection of Mulder continues our strategy to expand our pool of allrounders against top-quality opposition. He is a batting allrounder and his selection will depend on how we decide to balance our starting XI. He has been the top allrounder in the Sunfoil Series with a batting average of 60 (one century) and 15 wickets at an average of 28."
Squad Faf du Plessis (capt), Hashim Amla, Temba Bavuma, Quinton de Kock, Theunis de Bruyn, AB de Villiers, Dean Elgar, Heinrich Klaasen, Keshav Maharaj, Aiden Markram, Morne Morkel, Wiaan Mulder, Lungisani Ngidi, Vernon Philander, Kagiso Rabada.