The cyclone was reclassified as a category two storm - down from a category three - as it neared the Australian territory.
The system was predicted to pass over or near the island about 9pm Norfolk Island time (2000 AEDT) on Saturday, bringing destructive winds and very heavy surf.
The Bureau of Meteorology said Gabrielle was moving quickly at 6pm and was about 105km west-northwest of the island, home to around 2000 residents.
"Gale-force winds and high waves are likely occurring around parts of the island, and conditions may worsen overnight as the centre of the cyclone moves past," the bureau said.
There were already reports of downed trees and widespread power outages by 7pm, according to the ABC.
There were some indications that the island might avoid the system's strongest winds, however, a period of destructive winds with gusts up to 140km/h was still possible during Saturday evening or early Sunday.
Senior meteorologist Dean Narramore warned of bursts of heavy rainfall and very large seas and swell.
"These winds and rainfall are likely to bring down trees and powerlines (and) could cause some property damage as well as very dangerous and treacherous driving conditions," he said.
"We expect the centre of the circulation to move across Norfolk Island overnight and then start moving away from Norfolk Island (in the) early hours of Sunday morning.
"But on the backside, we expect another burst of strong to destructive winds as well as some bursts of heavy rainfall and a continuing damaging surf and swell."
Gabrielle should have weakened by Sunday afternoon and be well southeast of Norfolk Island, but surf conditions would remain hazardous through Sunday, Mr Narramore said.
A hazardous surf warning was in place for the Fraser Island coast, and waters off Sunshine Coast and the Gold Coast until midnight on Sunday.
The bureau was urging people to consider staying out of the water and avoid walking near surf-exposed areas, and for boaters to consider delaying their voyage if they planned to cross shallow water and ocean bars.
Tourists were urged to leave ahead of the storm, but Norfolk Island administrator Eric Hutchinson said anywhere between 800 and 950 visitors likely remained on the island.
"We are well prepared and we have just got to see this through, and then we will look at what resources are going to be needed in a recovery phase from tomorrow," he told ABC TV.
Teams of military and emergency personnel are on standby to respond as needed.
An emergency evacuation centre was made available on Saturday morning.
Mr Hutchinson said a cyclone of similar strength last passed over Norfolk Island in the mid-1990s, and residents were bracing for damage.
"We are expecting power outages, trees coming down, the potential for houses to lose roofs," he said.
Mr Hutchinson said he was most concerned about damage to visitor accommodation and the island's hospital, but there were contingency plans in place to deal with those events.
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.
Low to severe intensity heatwave conditions were expected in central and southeast Queensland at the weekend and into early next week.
33°C