The two families at the Mercure Hotel were in adjacent rooms.
Premier Mark McGowan said genome sequencing showed the cases were linked to each other.
“Unfortunately, transmission inside hotel quarantine facilities is not new,” he said.
“We are seeing it across the country and that’s why we need to do everything we can to consistently improve our systems.”
The two families will remain in place until they have recovered, unless they require hospitalisation.
Other guests on the floor have been moved elsewhere to remove any “unnecessary risk”.
Two people who were in adjacent rooms during the potential exposure period have been ordered back into quarantine for another 14 days.
Others on the floor must immediately self-quarantine and be retested.
Mr McGowan said the sheer number of new arrivals is a “major logistical challenge”.
“We currently have nine hotels with more than 2000 overseas arrivals on any given day,” he said.
“Unfortunately, we’re seeing more and more positive cases as the pandemic rages around the world.”
Two new cases have been diagnosed from hotel quarantine today, one from Egypt and one from India.
“India is obviously full of COVID,” he said.
“We have some evidence – that people are leaving Australia and going to India and then returning COVID-positive.
“This doesn’t seem to be a fair, reasonable or sensible thing that people are able to leave Australia currently and go to a country that is full of COVID and then return back.”
Mr McGowan said people should not be going to India “except for the most extreme of circumstances”.
He said under the current intake of returning travellers, it was not possible to space them out further in the hotels.
“The only way we can leave hotel rooms half empty is to halve the number of returning Australians,” he said.
“And obviously that creates a whole other set of issues because there’s people then overseas who want to come home who can’t.”
This content first appear on 9news