The cyclone was reclassified as a category-two storm - down from a category three - as it nears the remote Australian outpost.
The centre of the cyclone is predicted to pass over or near the island on Saturday evening, bringing wind gusts of up to 155 km/h and very heavy surf.
The Bureau of Meteorology said Cyclone Gabrielle was moving quickly on Saturday morning and was located about 325km northwest of Norfolk Island, home to around 2000 residents.
"Gale-force winds and high waves are currently developing and conditions are expected to worsen throughout the day as the centre of the cyclone approaches this evening," it said.
As the eye of the cyclone passes over the island, destructive winds may ease for a short period before regenerating, blowing from the opposite direction.
Teams of military and emergency personnel are on standby to respond as needed.
Tourists and visitors have been urged to flee, with the last flight leaving the island on Friday afternoon.
Norfolk Island emergency controller George Plant told AAP the community had been hard at work preparing for the storm impact.
"In times like this, the community just gets together and does what's required," he said.
An emergency evacuation centre will be available on Saturday morning. Seas are expected between five and seven metres, with peak waves possibly higher.
New Zealand's Met Service expects the cyclone to weaken to a tropical low before it moves towards the North Island on Sunday, although it is predicted to deliver severe wet and windy weather to regions including flood-hit Auckland.
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