Six crew members from a live export ship off Perth have tested positive for coronavirus, taking the state's total case numbers to 570.

Premier Mark McGowan fears the infection numbers from the vessel could rise further, labelling the situation as "extremely concerning".

"For the time being, the remaining 42 crew members, who I am advised are currently well, will remain onboard the ship and will be monitored and undergo health assessments as required," he told reporters.

"But I suspect it is probably more than likely that more crew members may become infected with the virus. This is an extremely concerning situation that we find ourselves in."

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The live export ship, the Al Kuwait, departed the United Arab Emirates on May 7.

Seven of the 48 crew members were tested this morning, with the six confirmed cases being removed from the vessel and placed in a Perth hotel for quarantine.

"Straight away, I had thoughts of the cruise ship saga," WA premier Mark McGowan told reporters, referring to the Ruby Princess disaster.

"I'm advised the ship was granted to enter the Port of Fremantle by the Commonwealth Government on May 23. At that time three crew members reported elevated temperatures.

"On May 22, the ship provided an updated report to Australian Border Force which included one crew with a high temperature and three showing similar symptoms in the last 15 days. This was when the final clearance was provided by the Commonwealth for the ship to berth.

"At this point, the Fremantle Port Authority was not made aware of the health concerns. A Fremantle Port worker, wearing PPE, went onboard the ship on the 22nd to help steer her into a berth at the port as per the usual process.

"This person, and any relevant close contacts, are now in isolation. It wasn't until Sunday evening that the Fremantle Port Authority learnt of some health issues on the ship. This came by word of mouth from another worker at the port. This information was then reported through the usual channels.

"And now we find ourselves in this situation. We're working as quickly as possible to get to the bottom of the situation. Clearly, this is not good. We want to get to a resolution as soon as possible so that the ship is in a position to leave the port."

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Covid19.govt.nz: The Government's official Covid-19 advisory website