The two sides said as they had recently returned from overseas travel in the last 14 days they responded to Prime Minister Jacinda Adern's suggestion that they should self-isolate.
The Chiefs said in a statement: "As a result, the Chiefs team and management will take the cautious approach and support the public effort to minimise risk.
"Effective immediately, all members of the Chiefs squad and managed who travelled to Sydney for the Waratahs match now enter self-isolation until Sunday.
"If the situation changes, in accordance with the advice of public health authorities, we'll adjust accordingly," it said.
They also advised the public that as not all their players or management travelled to Sydney they should not be alarmed if some of them, who were not required to go into self-isolation, were seen out in the public.
The Crusaders issued a similarly-worded statement but did not say how long they would be in self-isolation.
South Africa's director of rugby Rassie Erasmus and Springboks head coach Jacques Nienaber are continuing to work with the scheduled Test programme in mind. This is in spite of not being able to work with any of their players.
Erasmus told South African media, "All of us in the game across the globe are in the same boat. No one could prepare for the Covid-19 pandemic.
"Our planning for the season will carry on regardless, whether it's the Boks, Junior Boks, Blitzboks or our national women's teams. We still have a lot to prepare for," he said.
Camps across the country with the Super Rugby sides have been cancelled.
"While there are challenges when it comes face-to-face interaction with players and team activities, modern communication methods make it possible for coaches, players and management teams to keep in constant contact with one another," he said.
One consequence of the global shutdown is the effect it could have on the scheduled 2023 World Cup draw in November.
Teams could miss out on the chance to improve their rankings and, therefore, their prospect of getting a better seeding.
The failure to finish the Six Nations tournament, and the cloud hanging over the July Test window, will have consequences for those teams below the top four (South Africa, New Zealand, England, Ireland) and could result in the creation of a 'pool of death'.