The underwater volcano erupted on Saturday, about 65km (40 miles) north of the capital Nuku'alofa.
The eruption, which was heard as far away as the US, caused waves higher than a metre to crash into Tonga.
Local authorities have not confirmed any deaths but communications are crippled, making it difficult to establish the scale of the destruction.
However, the brother of a British woman said she died after being swept away in the waves. Angela Glover, 50, was washed away while trying to save her dogs.