Houses in the capital, Port Vila, were destroyed and "people are wandering the streets looking for help", said Tom Skirrow of Save the Children.
He said eight people were confirmed dead, but UN agencies say dozens may have been killed.
Vanuatu's president said he had a "heavy heart" and appealed for aid.
Pam has brought winds of up to 270km/h (170mph) and torrential rain.
The cyclone whipped up huge waves to batter the coasts of the archipelago
Australian Foreign Minister Julie Bishop said the country was preparing to send a crisis response team to Vanuatu if needed.
"There are destructive winds, rain, flooding, landslides, sea surges and very rough seas and the storm is exceedingly destructive there,'' she said. "We are still assessing the situation, but we stand ready to assist."
Although thousands of people spent the night in emergency shelters, many more were forced to ride out the storm in their own homes.
All six provinces of Vanuatu have been under red alert, meaning people are advised to immediately seek shelter.
Located about a quarter of the way from Australia to Hawaii, Vanuatu has a population of 267,000 spread over 65 islands. About 47,000 people live in the capital, Port Vila.
Pam, a category five tropical storm, had already caused major damage on other Pacific islands, including Kiribati and the Solomon Islands.
Tuvalu, a group of nine tiny islands north-east of Vanuatu, has also declared a state of emergency after the cyclone caused flash floods there.
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