The New South Wales government said it had made the "difficult decision" as it battles the highly transmissible Delta strain.
A stay-at-home order was issued on 26 June.
But clusters have emerged after some people who were found to be infected left their homes for essentials.
The outbreak of around 330 cases is the worst in the city this year.
A stay-at-home order covering more than five million residents in the Greater Sydney, Wollongong and Central Coast areas was due to be lifted on Friday. It has now been extended to 16 July. Schools will also be closed next week.
The New South Wales government said it recognised the "pain and stress" that lockdown was causing families and businesses.