However, its inbound flight, while delayed, is currently en route and expected to arrive at 12:30pm.
The Ministry of Foreign Affairs and Trade (MFAT) has sent a message to all Safe Travel registrants in Fiji regarding the incoming cyclone.
It's advised Kiwis to stay up to date with the latest information.
"We are advising New Zealanders in Fiji to follow any instructions (including any evacuation orders) issued by the Fiji authorities and keep their family in New Zealand informed of their well-being.
"Visitors and tourists staying in travel accommodation should follow the guidance of the accommodation management and/or tour operators."
New Zealanders in Fiji are strongly encouraged to register their details with the Ministry of Foreign Affairs and Trade at www.safetravel.govt.nz.
Oxfam is monitoring the cyclone closely and ready to give humanitarian assistance if required.
Its Fiji head Dolores Devesi said flooding and the threat of Cyclone Zena would put extra pressure on those still in recovery.
"The flood waters and threat posed by Cyclone Zena's gale force winds are the last thing Fijians recovering from Cyclone Winston need.
"We have humanitarian workers with emergency supplies on the ground, ready to respond, but supplies are limited and we need more assistance from the public."
While Cyclone Zena is yet to touchdown in Fiji, torrential rain has already hit the nation causing widespread flooding and the death of at least one person.
The Fiji Broadcasting Corporation reported a 70-year-old man was found floating in the Sabeto River yesterday morning.
Meanwhile a 19-year-old girl was reported missing after being washed away by strong currents in the river on Fiji's main island of Viti Levu.
Numerous roads have been closed and people living in temporary shelter have been told to seek safety elsewhere in a nearby evacuation centre.
People throughout the country were still picking up the pieces left behind from Cyclone Winston lashing the country just a few weeks ago, when the government issued a fresh storm alert.
Warnings have gone out for the central Lau and Lomaiviti island groups to prepare for damaging winds and flooding as Zena tracks towards the disaster-ravaged Pacific Island nation.
The latest alert says the Category 1 cyclone was 900km to the north west of Nadi earlier today, intensifying as it approached. The cyclone was expected to sit 150km south-southeast of Nadi at 3am tomorrow.
At the moment, average wind speeds at Zena's centre were 85km/h with gusts of 120km/h.
A gale warning was in force for Viti Levu, Kadavu and Mamanuca group with strong winds expected across the rest of Fiji.
All schools in the country have been closed until further notice.
Fiji's education minister Doctor Mahendra Reddy says further announcements would be made when the cyclone had passed Fiji.
Meanwhile, adding to the list of woes is Fiji being added to the Zika Virus Travel Warning list.
The Centre for Disease Control yesterday added the Pacific Island nation to its list of countries affected by the disease.
Transmitted by mosquitoes, the virus manifests similar to the flu, but there've been concerns that pregnant women could transmit the disease to their unborn babies, with serious consequences.