"Disaster tourists" are making it harder for firefighters to tackle the Port Hills blaze, authorities say.
The fire, which broke out about 2pm on Wednesday, has burnt through more than 630 hectares and caused the evacuation of 110 homes.
Eighty firefighters were at the scene and 12 helicopters were in the air, dumping water on the flames.
At a press conference on Thursday, Canterbury police Inspector Ash Tabb said "disaster tourists" were blocking emergency services from doing their jobs.
"People are going into the area to have a look and they are making it very hard for all those involved in the firefighting."
Tabb said they were blocking roads, preventing crews from moving large firefighting and earthmoving equipment onto the fire ground.
They were also preventing residents from returning to their homes to collect belongings.
"They can't get to their own houses or get away because of people sightseeing on the roads."
Tabb asked members of the public to stay away:
"Let the firefighters do their job and let the community enter the area if required."
Emergency Management Minister Mark Mitchell also asked for people to stay out of the area.
During a fire in Tasmania in 2018, he said, "some brain surgeon" put a drone up to capture images.
That posed an "extreme" risk to helicopter pilots, he said.
"They actually have to land the aircraft and it interferes with the fighting of that fire.
"Those actions will be met with serious consequences."
According to the ABC, helicopters had to cease waterbombing the bush fire due to the drone.
Helicopters fighting the fire in Lee Valley, Tasman last week also had to be grounded for half an hour because of a drone.
Six were stood down due to a drone sighting in the area and a seventh helicopter was also stood down before it reached the scene of the fire.
Fire and Emergency Incident Controller Steve Trigg said at the time drones were a safety risk to aerial firefighting, as a mid-air collision with a drone could have fatal consequences.