The South Africans cited player welfare concerns because of the delayed start to their domestic competition and uncertainty over government travel restrictions during the COVID-19 pandemic affecting players based in South Africa, Europe and Japan.
"With time essentially having run out, it left us with no option," SA Rugby chief executive Jurie Roux said in a statement on Friday. "This is a hugely disappointing outcome for our supporters and commercial partners but the on-going impacts of the pandemic ... means we are unable to deliver a Springbok team without seriously compromising player welfare."
Roux said SANZAAR, the tournament organisers, and hosts Australia "have bent over backwards to make the tournament happen and it would have been unfair on them, their partners and state government to delay a decision any longer.
"The impact on our planning was profound and took us to a bottom line that we could not in fairness commit to being able to compete."
The South Africa-based Springboks players had been scheduled to leave for Australia on Sunday and play their first test against Argentina in Sydney on Nov. 7, more than a year since their previous Test match. South Africa are due to host the British and Irish Lions next year and might have gone without Test rugby for 20 months by the time that series starts, unless new Tests can be scheduled.
The Springboks would now have to "find ways" to be ready for that series, Roux said.
South Africa's provincial Currie Cup competition only began on Oct. 9 because of the delays brought on because of the coronavirus, leaving Springboks players with little match play before the Championship.
At most, South Africa's home-based players would have had three domestic games before the team's scheduled departure for Australia and two of those would have been informal or exhibition matches.
The decision to withdraw was supported by the body that represents the interests of South Africa's players, SA Rugby said.
The Springboks' withdrawal will cut the Rugby Championship from 12 to six matches, which still will go ahead over a six-week period with each team having at least two byes. The re-branded Tri-Nations tournament will also likely hit broadcasting revenue, which will be shared among the three competing teams.
The Argentina squad is already in Australia preparing for the tournament, its preparation at home set back by a COVID-19 outbreak which affected at least 10 players and the head coach. The Pumas will also be short of match play when they face their opening Test and are attempting to arrange warm-up matches against local teams.
The All Blacks and Wallabies will meet in the opening matches of the tournament in Sydney on Oct. 31 and Nov. 7, following on from their two-match Bledisloe Cup series in New Zealand.
Revised Tri-Nations tournament schedule:
Oct. 31: Australia vs. New Zealand, Sydney.
Nov. 7: Australia vs. New Zealand, Brisbane.
Nov. 14: New Zealand vs. Argentina, Sydney
Nov. 21: Argentina vs Australia, Newcastle.
Nov. 28: Argentina vs New Zealand, Newcastle.
Dec. 5: Australia vs. Argentina, Sydney.