Agriculture minister Adam Marshall was told on Thursday that he had tested positive after dining with three government colleagues at a Sydney restaurant on Monday, which an infected person had visited earlier.
All four had been attending Parliament as recently as Tuesday.
Health minister Brad Hazzard said he was self-isolating after being exposed to a potential case at Parliament House.
Mr Hazzard said that, while standing next to premier Gladys Berejiklian at daily pandemic media briefings, he thought she was “fairly safe”.
Pandemic restrictions tightened in Sydney on Thursday as a cluster of the delta variant, first identified in India, increased and states banned travel from either parts of Sydney or from anywhere in New South Wales.
The cluster, which had grown to 31 cases by yesterday, began last week when a Sydney airport limousine driver tested positive. He was not vaccinated and is suspected to have been infected while transporting a foreign air crew.
Police were considering charging the driver and his employer with a range of offences, a spokesman said.
Ms Berejiklian said: “Since the pandemic has started, this is perhaps the scariest period that New South Wales is going through.
“It is a very contagious variant but at the same time we are at this stage comfortable that the settings that are in place are the appropriate settings.”
Australian states have closed their borders to travellers either from parts of Sydney or from anywhere in New South Wales and New Zealand has stopped quarantine-free travel from New South Wales for at least three days.
Victoria state said it would continue to ease pandemic restrictions in its capital Melbourne following a fourth lockdown, despite a Melbourne resident testing positive after returning from Sydney on Sunday.
Australia has been relatively successful in containing coronavirus clusters, although the delta variant is proving more challenging.
The pandemic has claimed 910 deaths in Australia, which has a population of 26 million.
The only Covid-19 death since October was an 80-year-old man who became infected overseas and was diagnosed in hotel quarantine.