Extra testing clinics were set up after Victorian health officials notified NSW Health the person visited Jervis Bay, Goulburn, Hyams Beach and Vincentia on May 23 and 24.

The man had some symptoms on May 25 after driving back to Melbourne on May 24. He tested positive on Monday, nearly a week later.

NSW recorded no new cases of community transmission on Wednesday, but the man's wife and child have also since tested positive.

Chief Health Office Kerry Chant said NSW Health was working with Victorian authorities to determine who in the family contracted the virus first.

"If this gentleman was the source for those individuals, then they were not potentially infectious when they were in NSW, and clearly if the reverse is the case that may take back the exposure period," she told reporters on Wednesday.

Already 243 people have been instructed to get tested and isolate while they await further instructions from NSW Health.

"We've asked (them) to stop and stay until we actually really understand and do a full assessment of the risk," Dr Chant said.

The venues of concern include the Green Patch campground and Booderee National Park at Jervis Bay, the Cooked Goose Cafe at Hyams Beach, Coles Vincentia Shopping Village and Trapper's Bakery and Shell Coles Express Big Merino at Goulburn.

Parks Australia have since announced Booderee National Park will shut until at least midday on Friday.

The popular Cooked Goose Cafe has also closed for deep cleaning with the owners and eight staff in isolation.

Victorian authorities have flagged they believe the strain circulating in the state is much more infectious than previous variants, capable of transmitting between strangers with very minimal contact.

Those concerns prompted the Victorian government to extend the lockdown for Greater Melbourne for at least another seven days until midnight on June 10.

However, Dr Chant downplayed those fears, saying NSW has also had occasions we have had transmission with very minimal contact.

"In some circumstances sometimes COVID can be transmitted by very minimal contact."

"(But) clearly this appears to be a more transmissible strain in general."

Despite restrictions lifting for people in regional Victoria, Premier Gladys Berejiklian said the NSW border will remain open.

As with previous lockdowns, anyone travelling to NSW to escape lockdown conditions would find themselves forced to abide by them here, Ms Berejiklian said.

Local MP Shelley Hancock said the news a case had visited the South Coast with a highly contagious strain was "super alarming" and is concerned about the impact of an outbreak on the area's elderly population.

"Sometimes complacency sets in - well, here's the wake-up call," Ms Hancock said.

The premier echoed that message, urging NSW residents to come forward for testing.

"They know the drill when there are cases in other parts of Australia," Ms Berejiklian said.

"We've seen more than 21,000 people come forward in the last 24 hours in NSW and get tested - that's outstanding."

She also urged NSW residents to get vaccinated as soon as they're eligible.

Australian Associated Press