The man, who was reportedly a painter on the $150 million Goulburn Base Hospital redevelopment, was infectious while at work on Friday, July 9 and was isolating from the following day. He had travelled from Fairfield in southwest Sydney.

It has prompted a flurry of testing of contractors and hospital staff.

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Cr Kirk said the council was advised that the worksite had been closed down, all workers had been sent for testing and the site wouldn't re-open until all tested negative.

But the Mayor says it rightly raises the question - what is an essential worker?

"How is a painter an essential worker who qualifies for an exemption to travel from southwest Sydney to the region?" he said.

"If this was needed so badly, surely we could have found a local. I don't accept that just because he's working on the hospital there's a need to travel outside those hotspots...Obviously the definition is too loose."

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He spoke to Goulburn MP Wendy Tuckerman on Tuesday morning about enforcing a more "rigid definition" of an essential worker and enforcement around this. Ms Tuckerman in turn spoke to Premier Gladys Berejiklian, resulting in a new Public Health Order. It requires essential workers who leave Fairfield for essential work to get tested for COVID-19 every three days, and people from Greater Sydney to undergo weekly tests.

The council advised that two men had called in to Marulan's Hungry Jack's while potentially infectious on Saturday, July 10. It was closed for deep-cleaning on Tuesday.

Cr Kirk said the next 48 hours of testing and contact tracing would be critical in revealing the extent of the hospital contractor's infection.

"They are mostly external subcontractors working on the site but there are locals there as well and the concern is that they've come in contact," he said.

"Let's hope it's confined to this worker, that it hasn't spread too far beyond that."

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The Mayor expressed his frustration after receiving reports from business owners on Friday that Sydney people were travelling to Goulburn. When they had been challenged about breaching the lockdown, they had told business people that they were bored and wanted to go for a drive.

"They were quite blase about it so this is the level of disregard that people are paying to the stay at home orders," he said.

"Without a doubt, there are so many people ignoring the orders and think they can just go for a drive. Goulburn is a popular stopover and it is raising a whole lot of concerns. I'm worried about people calling into service centres in and around Goulburn and that we'll potentially have another incident like Trappers Bakery (in June) or worse."

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