The new measure applies to all Greater Sydney local health districts, except for the Illawarra, Shoalhaven, and the Central Coast.
Emergency surgeries and urgent elective surgeries will not be affected.
There are currently more than 2,500 active cases of COVID-19 across NSW, with the greatest concentration in western and south-western Sydney.
Rates of hospitalisation have also climbed in recent days, with 187 patients now being treated in hospital.
Of these, 58 are in Intensive Care Units and 24 require ventilation.
It is the first time non-urgent elective surgeries have been suspended in NSW since the early stages of the pandemic in March last year.
In a statement, NSW Health said hospitals continue to have sufficient capacity for treating the seriously ill with 500 ICU beds available throughout the system.
Health authorities also have the capacity to quadruple current ICU capacity, if required.