Health Minister Roger Cook confirmed on Sunday that Patricia Oldendorff was on her way to the Indonesian coal loading port of Tanjung Bara.
The ship with 20 Filipino nationals and the captain arrived from Manila on September 16 and was anchored eight nautical miles off Port Hedland.
Eighteen of its crew members contracted the virus but have since recovered.
According to WA Health, 12 of the rescued crew members had returned to the ship before sailing, while three colleagues still to be clarified were flown to Perth and are now in hotel quarantine.
It arrives as an unwell crew member aboard a Panama Bulk Oil Carrier given a weak positive test after it had come ashore.
The Vega Dream was anchored off Port Hedland on Friday after sailing from Shanghai via Manila, Cook said.
It picked up cargo on Saturday night when the man was feeling uncomfortable.
He was taken to a local hospital where, after initial rapid tests, he gave a weakly positive result.
“His samples are now being flown to Perth so we can review the results of this earlier test,” Cook told reporters on Sunday.
Mr Cook wasn’t sure how many crew members were on board but said no one else was suffering from symptoms.
“We don’t currently know if they have gathered additional crew members in Manila,” he said.
“But it has been on sails for many weeks – I now think over 16 days.”
He assured the WA public that the ship posed no health risk and hoped that it would set sail later on Sunday.
“These oil carriers come to rest a good 12 meters from the dock,” said Cook.
“We do not believe that there is a risk of infection for the dock workers or the community.”
There are no plans to send WA Health personnel aboard the ship to test other residents until the crew member’s initial test result is verified.
Mr Cook said the federal government needs to make sure it is working with its international partners to ensure that “these situations do not continue to arise”.
WA recorded two new cases – a man and a woman in hotel quarantine – on Sunday when the state had no community transmission for six months.
“It shows that the measures we have taken, including our hard border with the east, have worked,” said Prime Minister Mark McGowan.
People in Australia need to be at least 1.5 meters away from others. Check your state’s restrictions on collecting limits.
If you are experiencing cold or flu symptoms, stay home and schedule a test by calling your doctor or contacting the Coronavirus Health Information Hotline on 1800 020 080.
News and information are available in 63 languages at sbs.com.au/coronavirus.
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