A woman who travelled on the flight from Doha last week said she received the document in an email from WA Health.

It contained the personal information of 47 passengers who sat near each other on the flight, including their names, addresses and passport numbers.

"There was one name highlighted which was also shocking," the woman told ABC radio on Wednesday.

"I didn't want to make assumptions but I can only assume that was the (infected person)."

WA Health said it believed the data breach involved "the accidental release of the wrong document" by the North Metropolitan Health Service, which would further investigate the incident.

"We take medical confidentiality very seriously and we apologise for what we understand to be a breach, and a thorough investigation will be undertaken," a spokesperson said.

"WA Health and the North Metropolitan Health Service apologise unreservedly to those affected."

Passengers who sat near the suspected infectious case were considered low risk but should monitor for symptoms.

"Monkeypox is difficult to transmit and there is no risk to the community," the spokesperson said.

Opposition health spokeswoman Libby Mettam said the breach was deeply concerning.

"This alleged breach is completely unacceptable and has undoubtedly compromised the safety and security of those passengers, and those affected have every right to feel aggrieved," she said.

"It raises concerns about who else has access to this information and warrants a full and thorough investigation into both the breach and the wider processes within the department when handling confidential information."

Two unrelated monkeypox cases have so far been confirmed in WA since the virus arrived in Australia.

The virus is spread through skin-to-skin contact or from touching contaminated objects, including bedding, towels or clothes.

Symptoms include rashes, lesions or sores - particularly around the genitals - as well as fevers, aches and swollen lymph nodes.

Australian Associated Press