Defence Minister Peter Dutton confirmed the request had been approved.
"Up to 300 Defence personnel will deploy in the coming days to assist NSW authorities with COVID-19 restriction compliance measures," he said in a statement.
"Defence members will commence deploying on Friday 30 July to undertake training over the weekend and commence working under the direction of NSW Police on Monday 2 August."
But Cumberland City Council mayor Steve Christou said he was concerned about the prospect of the army being sent in, as it would cause anxiety among residents.
“If the army is going to be brought in to just enforce lockdown, I don't think it's going to be a good look at all," he said.
“I don't think people are going to accept it very well - our people are one of the poorest demographics, and as it is, they already feel picked on and marginalised, as if their whole life has been taken away from them.
"They can't afford to pay the mortgage, the rent, the food or work. Now to throw out the army to enforce lockdown on the streets is going to be a huge issue to these people.
“It's demoralising for a lot of people.”
He said it would be a different scenario if the army was to help Western Sydney health centres and with logistics.
The Australian Lawyers Alliance also raised concerns that such "extraordinary measures" could set a "dangerous precedent".
Spokesman Greg Barns SC called on the government to explain what role troops would play in this deployment.
"Using the defence force to ensure compliance by Australians or to deter civil disobedience is a concerning use of our armed forces," he said.
“The role of any police or enforcement agencies should be to help meet the needs of residents so they don’t have to break the rules.”
Mr Dutton said more than 13,000 ADF personnel have so far been deployed around Australia as part of COVID-19 assistance operations, including over 1,300 troops across the country currently.
Almost 230 were supporting police quarantine, reception and repatriation efforts at Sydney airport and hotels.