As of Thursday, anyone returning to the ACT from Sydney hotspots or Victoria are now legally required to self-isolate for 14 days.

It comes after the number of cases connected to a Casula pub rose to almost 40. Health authorities believe the outbreak began with a man who traveled from Victoria.

The RUC in Turner asked patrons on Wednesday not to enter the club if they had been to south-western Sydney, particularly Campelltown and Liverpool, or Victoria in the past two weeks.

"We certainly do not intend to cause any offence, and we realise this is a difficult message, but we feel we have a responsibility to implement these measures," it wrote in a Facebook post.

Secretary manager Jeremy Wilcox said it was not a rule the club could easily enforce, but was in step with government health restrictions.

"It's more about asking our members to act themselves, rather than any sort of enforcement," he said.

"Everyone has got a role to play and we can assist by asking our members and guests not to come.

"We really want to move to stage three easing of restrictions in Canberra and anything that will help that process we're very happy to be part of."

The National Zoo and Aquarium has also taken a hard line approach. Signs are plastered around the site to remind anyone who has been in a COVID-19 hotspot in the past two weeks, they cannot enter.

Business manager Russell Jackson said about 20 bookings at the Jamala Wildlife Lodge had to be cancelled, but enforcing the rules on people entering the zoo day-to-day was near impossible.

"When it's up to people to disclose whether they've been in those locations in the last 14 days, that's where it gets a little more difficult," he said.

"We rely a lot on people, taking a common sense approach and volunteering the fact they had [been in a hotspot] and not going out in the first place."

Mr Jackson said the zoo had implemented some of the strictest measures out of concern for the diverse species it housed.

"No one is really sure which species and how exposed they are to COVID," he said.

"So we've taken the extremely cautious approach."

ACT Health Minister Rachel Stephen-Smith said it was a decision for individual businesses to take that "extremely precautionary approach".

"I don't know that banning people from entering businesses who've been in Sydney is going to be particularly helpful," she said.

"I would encourage businesses to implement their COVID safety plan and for those businesses where people stay for a period of time like restaurants and cafes, obviously keeping the name and contact number of everyone who attends those businesses is really important."

Canberrans have been urged not to visit the Sydney hotspots of Campbelltown and Liverpool.

Ms Stephen-Smith said it was a precautionary measure as there was not evidence of community transmission in those areas yet.