Richardson was added to Australia's ODI squad for their three one-day internationals in South Africa, with the first match to be played in Paarl on Saturday. But he did not make the cut for the squad announced Wednesday for the three-game series against the Kiwis in Australia starting March 13.
Australia has confirmed that the original 14-player ODI squad for the South Africa tour, not including Richardson, will be retained to take on New Zealand.
The 23-year-old Richardson was one of five fast bowlers picked in Australia's squad for the Twenty20 leg of the three-week tour in South Africa but has been overlooked for the first two games in that format.
The T20 series is tied ahead of third match in Cape Town later Wednesday. Australia won the series opener by 107 runs in Johannesburg but lost the second by 12 runs in Port Elizabeth.
Richardson could instead play a part in the one-dayers. He was set to be a pivotal player in the 50-over World Cup in England last year but injured his shoulder before the tournament and was sidelined for months.
"Jhye is performing exceptionally well," Australian selector Trevor Hohns said. "He has slotted back into the T20 squad in South Africa and is pushing for a place in that side."