There were no confirmed reports of deaths from the Category 4 storm that bought winds of around 200 km (125 miles) per hour, but there were a lot of injured people, some seriously, said Graham Kenna, an Australian government adviser at Tonga's National Emergency Management Office.
Photos posted on social media showed a wrecked Parliament House building in the capital, as well as extensive flooding and downed power lines. Access to areas outside the capital were hindered by the storm damage and debris.
"The full extent of damage caused by Cyclone Gita is still being assessed but there is an immediate need for assistance on the ground," NZ Foreign Affairs Minister Winston Peters said in a statement.
"About 5,700 people sought shelter in evacuation centres overnight, and it is expected these numbers will increase substantially tonight."
New Zealand is donating NZ$750,000 ($545,000) in aid, and a NZ Air Force Hercules aircraft was due to fly emergency relief supplies into Tonga on Tuesday.
Australia is donating A$350,000 ($275,000) worth of emergency shelter, kitchen and hygiene kits, while the country's foreign minister said the Australian Defence Force personnel would assist with clean-up efforts.
The cyclone was heading towards Fiji's southern islands on Tuesday, with some forecasts reporting it intensifying towards a Category 5 storm. Fijian Prime Minister Frank Bainimarama warned residents to "heed warnings and prepare", although the storm is expected to bypass heavily populated areas.
Gita had pummeled Samoa and American Samoa, about 900 km (560 miles) to the northeast, over the weekend, flooding the Samoan capital, Apia.