Victorian left-arm spinner Holland, 30, played two Tests for Australia against Sri Lanka in mid-2016, but was passed over in the recent 4-0 Ashes Test series win over England.
Richardson, 21, is one of five pace bowlers in the Australian touring party for the four-Test series and the No.2 ranked South Africans.
Holland was the outstanding spinner in the Sheffield Shield last season and was named man of the match as Victoria claimed their third straight title.
"We envisage the wickets we will see in South Africa will not warrant the need to play two spinners.
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"But should Nathan Lyon not be able to play at any stage, we wanted to have the best specialist spinner available to us and based on current red ball form Jon warrants that spot."
Hohns said Richardson warranted his inclusion in the Test squad for the first time.
"Jhye is a talented right-armer who bowls with very good pace through the air," he said.
"He is an exciting young prospect who will benefit immensely from his time with this squad."
Opener Cameron Bancroft held his place in the Australia team despite an indifferent Ashes series against England where he scored 179 runs at 25.57.
Peter Handscomb, dropped after the second Test in the series after scoring just 62 runs, is retained as a back-up batsman.
Cricket Australia said all members of the Test squad will head to South Africa on February 15, with the exception of David Warner, who will captain the Australian T20 International side.