The storm system is bringing wind gusts up to 150 kilometres at its centre.
Tonga has declared a state of emergency as the cyclone passes near the northern island of Vava'u.
Carlos Calderon from Oxfam New Zealand said the key priority will be ensuring a clean water supply and the emergency needs of residents are met.
"Cyclone Ula is hitting Tonga with very destructive winds and there is a risk of high seas causing flooding in low-lying areas," he said.
"We have emergency supplies in Tonga ready in place, so once the urgent needs are assessed we are ready to help coordinate the supply of clean water and sanitation for those affected by the disaster."
Mr Calderon said the economic livelihoods of residents are particularly at threat as the storm is forecast to destroy crop harvests.
In January 2014, Tropical Cyclone Ian ripped through the Ha'apai islands in Tonga, wiping out buildings and homes.
Laitia Fifita from Tonga's Met Service on Tongatapu said flash flooding is expected in Vava'u.
"It is expected that the speed of movement of the tropical cyclone will speed up a little bit, so at around midday today it is expected to lie further west out of from the island of Vava'u and continue on a south southwest direction," he told .
Gale force winds of up to 200 kilometres per hour and torrential rain have been forecast.
Category-three cyclone Ula moves over Tonga Source: Fiji Meteorological Service
A damaging swell is expected to develop overnight with the risk of "very high to phenomenal seas".
Tonga's Tropical Cyclone Warning Centre said the cyclone is strong enough to cause extensive property damage, crop damage and power blackouts.
Tonga Meteorological and Coast Radio Services said warnings remain in place for Vava'u, Ha'apai, Tongatapu and Eua.
Residents in Vava'u have been told to prepare for "possible flash flooding".
Cyclone Ula is forecast to hit Fiji's Lau group next.
Residents have been told to expect rain, thunderstorms and heavy swells from Saturday night, before the category 3 system makes landfall on Sunday morning.
Fiji rugby Sevens coach Ben Ryan posted on a message on Twitter, urging those affected by the cyclone to take care.
