The Hunga Tonga-Hunga Haʻapai 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.
There have not yet been any confirmed deaths but communications are crippled, making it difficult to establish the scale of the destruction.
Friends and family of British woman Angela Glover say she is missing. In social media posts, they say she was swept away in the waves.
More than 10,000km away, two people drowned off a beach in northern Peru amid abnormally high waves.
Both New Zealand and Australia sent surveillance flights to find out more, with New Zealand saying there had been "significant damage" along the western coast of Tongatapu, Tonga's main island.
Internet and telephone communications in Tonga are extremely limited and outlying coastal areas remain cut off.
For Tongans living overseas, it has been two days since they have been able to speak to family and friends.
Petilise Tuima told the Sydney Morning Herald that the last time she spoke to her family was on Saturday afternoon when they were fleeing to higher ground.
"Everyone is calling each other within our Tongan groups, wanting to see if anyone has picked up or heard anything... We are just desperate," she said.
The Ha'atafu Beach Resort on Tongatapu was "completely wiped out" and "the whole western coastline completely destroyed", according to a post on the resort's Facebook page written by contacts overseas.
The post said those living there "just managed to get to safety running through the bushes and escaping", and were "not able to save anything".
The Pacific correspondent for Television New Zealand, Barbara Dreaver, wrote on Facebook that it would take "at least two weeks before international phones and internet are working again", due to damage inflicted on a critical submarine cable as a result of the volcanic eruption.
The Red Cross said even satellite phones, used by many aid agencies, had poor service due to the effects of the ash cloud. The organisation estimates that up to 80,000 people may have been affected by the tsunami.
The dust from the volcano could contaminate water supplies, with locals advised to drink bottled water and wear masks.
Some officials have voiced concerns over relief efforts resulting in a spread of Covid in the country, which only recorded its first case in October.
"We don't want to bring in another wave - a tsunami of Covid-19," Tonga's deputy head of mission in Australia, Curtis Tu'ihalangingie, told Reuters.
Tonga is made up of 170 islands scattered over about 700,000 sq km. About 100,000 people live in Tonga, the bulk of them on Tongatapu Island.
