The 53-year-old is in intensive care in a stable condition. He was one of three cases diagnosed in NSW on Monday. A man who returned from Iran on Saturday was confirmed with the disease, and his sister also infected. The sister and the healthcare worker are the first known person-to-person cases in Australia.

NSW Health Minister Brad Hazzard said people should stop shaking hands and be cautious about who they kiss.

"It's time that Aussies gave each other a pat on the back for the time being, no hand shaking," he said.

Iran is proving the new flashpoint for Australia, with six cases confirmed in the past few days among people returning from Iran, on separate flights.

Tasmania also confirmed its first case on Monday, in a 40-year-old man who returned from Iran. The man flew on a Virgin flight from Melbourne to Launceston on Saturday.

That leaves the ACT and the Northern Territory the only jurisdictions yet to report a case. Three cases among people returning from Iran have been reported in NSW, and one in each of Queensland, Victoria and Tasmania.

The latest cases come on top of the 15 early cases connected with the Wuhan tour group, all of whom have recovered, and 10 from the Diamond Princess cruise ship, one of whom became the first Australian to die from the virus.

The states are now tracing contacts of the Iranian cases, including people shared a Qatar flight from Doha to Sydney on Saturday with a woman who became sick almost immediately. Health Minister Greg Hunt said Queensland had set up a dedicated respiratory clinic where people could go to be tested.