The number of confirmed cases of COVID-19 in the Illawarra Shoalhaven Local Health District had jumped to 26 by midday Monday.
The district's public health unit is contacting people who have been in close contact with any of the confirmed cases and asking them to self-isolate for 14 days from their last contact with the case, or to be tested if they develop symptoms.
The unit will follow up with confirmed cases on a daily basis, and support them with ongoing advice.
Health authorities urged anyone who'd been overseas in the last 14 days and had symptoms, or had close contact with a confirmed case, to take advantage of the region's three COVID-19 assessment clinics at Wollongong, Shellharbour and Shoalhaven Hospitals.
And they encouraged everyone to play their part in containing the spread of the virus by practising personal hygiene measures such as thorough handwashing; avoiding close contact with anyone with cold or flu-like symptoms and keep their distance from others as much as possible by social distancing.
The NSW premier also urged the public to take personal responsibility to slow the spread of coronavirus, with police on standby if people fail to comply with the social distancing rules.
Gladys Berejiklian on Monday implored people to understand the seriousness of the COVID-19 outbreak after social distancing rules on the weekend were widely ignored.
"This is getting very serious and our actions have to match how serious this is," Ms Berejiklian told reporters in Sydney on Monday.
Her comments come as the number of COVID-19 cases in NSW jumped to 669 as of 8pm on Sunday - increasing by 136 cases in 24 hours.
This includes 48 confirmed cases among passengers on the Ruby Princess cruise ship, which docked in Sydney on Thursday, and five cases from the Ovation of the Seas ship, which docked a day earlier.
The premier said authorities on the weekend noticed not enough people were following the health advice and social distancing guidelines which is why a shutdown of non-essential services has been put in place from 12pm on Monday.
The NSW government decided on the new restrictions on Sunday before Prime Minister Scott Morrison in the evening announced that all state and territory leaders had agreed to a nationwide shutdown of "principal places of social gathering".
Ms Berejiklian said the state's police force is on standby if people fail to comply with the restrictions.
"We want people to take personal responsibility ... Your personal actions can result in someone getting very sick or dying," she said.
"If people fail to enforce, the police are on standby to deal with that."
While venues such as pubs, cinemas, gyms and churches will be closed from noon on Monday, schools in NSW will remain open.
Ms Berejiklian has, however, encouraged parents to keep their children at home if possible.
"The health advice has not changed however, for practical reasons, in NSW we will be encouraging parents to keep their children at home," she said.
"Already last week we had up to 30 per cent of parents who chose to keep students or their children at home and we appreciate and anticipate that number will increase."
NSW chief health officer Dr Kerry Chant on Monday said of the state's confirmed cases, 327 have been acquired overseas, 155 are from contact with other cases and 65 have been locally transmitted while the remainder are under investigation.
Dr Chant urged young people in particular to play their part and adhere to social distancing rules to protect the most vulnerable in the community.
NSW Health Minister Brad Hazzard said authorities were left with "no alternative" but to shut down non-essential services after hundreds of people ignored guidelines and flocked to Sydney's Bondi Beach at the weekend.