A thief has made off with 42,000 much-sought rapid antigen tests from a freight depot in Sydney, authorities said Wednesday.

A man entered a freight depot in the suburb of Mascot on Tuesday afternoon and "took possession of the tests", a New South Wales police spokeswoman said, without giving further details.

"Officers attached to South Sydney Police Area Command have commenced an investigation into the theft of Rapid Antigen Tests," she said. 

New South Wales Premier Dominic Perrottet condemned the incident, which took place as Australia faces a shortage of rapid antigen tests.

"At a time when everyone across our state has made incredible efforts in keeping people safe, in making sacrifices, what a disgraceful act," Perrottet said. "The police will catch you." 

The country's consumer watchdog has received reports of retailers selling tests for about US$22 each.

The Australian Council of Trade Unions this week threatened strike action if free rapid tests aren't provided to vulnerable workers. 

Prime Minister Scott Morrison on Wednesday defended his government's handling of test procurement.

"I understand that those rapid antigen test shortages have been a great frustration but a lot of these comments are made with hindsight, not foresight," he said. 

The government expects up to 52 million rapid tests will be flown into Australia this month from Asia and the United States.