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.