Authorities reported 16 new infections on Wednesday, which brings the cluster there to 37 cases.
Sydney's 5.3 million residents will have to wear masks indoors, and many will be banned from travelling out of the city.
Officials are concerned about the "extremely contagious" Delta variant.
The cluster marks the largest rise in infections in Sydney since December. For most of the year, locals have enjoyed almost no restrictions on daily life.
But the sharp case rise in the past week has prompted authorities to reinstate distancing rules.
"Please abandon non-essential activities, please don't attend social gatherings unless you absolutely must," said New South Wales (NSW) Premier Gladys Berejiklian.
From Wednesday, households will be limited to a maximum of five visitors. Restrictions will also be put in place at dining venues, gyms, sporting arenas and other gathering areas.
People who live or work in central and eastern Sydney will be banned from travelling out of the city.
NSW Health Minister Brad Hazzard said the virus risk had escalated to a "very real and present danger" right across Sydney.
The cluster of infections had initially centred around a shopping centre in Bondi, the popular beachside suburb and famous tourist destination in the city's east.
On Wednesday, authorities reported that cases had also been detected on the other side of Sydney, some 65km (40 miles) away from known hotspots.
The outbreak was also causing concern in New Zealand, after an infected person travelled from Sydney to Wellington.
New Zealand authorities introduced a number of restrictions on Wednesday, while the "travel bubble" that allows people to fly between the two countries was closed to passengers from Sydney.