The decision follows a raft of recent measures implemented to stop coronavirus transmission,including postponing events,closing indoor exhibits,going cashless and reducing the daily guest capacity for both zoos.
Face-to-face and community engagement programs have also been put on hold while the zoos work out what services can be delivered via digital platforms.
"We are committed to maintaining these measures for as long as public safety requires us,"Taronga said in the statement.
While both zoos will be closed to the public,essential staff will remain to care for the animals,including native fauna recovering in its wildlife hospitals following the summer bushfires.
Taronga said its veterinarians advised that while its animals could become infected with COVID-19,they were highly unlikely to become sick.
"Zoo animals,if infected,could be a source of virus that could transfer back to people,but this scenario is unlikely and they would be no more of a risk to public health than other people sick with the virus,"Taronga said.