The chopper was flying over Spaghetti Junction at just under 1400ft when the pilot spotted a drone about 10 metres away.
Police said in a release the crew were forced to take "immediate evasive actions to avoid a serious collision".
It is believed there were also two other unauthorised drones in the immediate vicinity.
"The pilot and crew ere left shaken after evasive action was taken."
Police suspended operations for the rest of the shift as a precautionary measure. The chopper was inspected and crew were interviewed by detectives.
Police are working with the Civil Aviation Authority.
Normal operations have resumed this morning.
"Our Police helicopter is responsible for saving lives and keeping our community safe," said Inspector Jim Wilson, acting District Commander for Auckland City.
"The actions of these people in flying a drone dangerously close to the Eagle helicopter is totally irresponsible and Police will investigate thoroughly."
"This could easily have ended in a tragedy and it is a worrying reminder of the dangers of flying drones near other aircraft."
The incident marks what was otherwise a mostly well-behaved New Year's Eve across the country.
