Cyclone Waka, registering wind speeds of up to 250 km (155 miles) per hour at its centre, left a trail of destruction on the kingdom's northern islands of Vava'u and Niuatoputapu.
In an appeal on Tongan television, the Red Cross said at least 200 houses have been severely damaged or destroyed in the Vava'u town of Neiafu, which is home to about 5,000 people.
A significant amount of food crops were destroyed with commercial crops such as kava also badly hit, Tongan officials said.
The Red Cross said it hoped to ferry food supplies to affected areas next week.
New Zealand Ministry of Foreign Affairs and Trade spokeswoman Jocelyn Prasad said New Zealand would supply water, food supplies and temporary shelter if Tonga asked for help.
There were no reports of any casualties from the storm but officials said it could take up to a month to restore electricity in some areas.
Tonga -- dubbed the Friendly Islands by British explorer Captain James Cook -- has a population of 100,000 spread over 170 coral islands in the South Pacific about 2,000 km (1,250 miles) north of New Zealand.
- Reuters - Thomson Reuters Foundation
- For more humanitarian news and analysis, please visit https://www.trust.org/alertnet