Japan has issued warnings of three-meter-high waves, and 1.2-meter-high waves have hit the country's south.
The United States issued a warning about strong currents and waves, as well as coastal flooding.
Tonga was hit by waves of more than a meter high as a result of the massive underwater volcanic eruption.
The eruption of the Hunga Tonga-Hunga Haapai volcano was heard all the way across the South Pacific, and eventually all the way to the United States.
Many parts of Tonga, whose capital is only 65 kilometers (40 miles) south of the eruption, are covered in ash and have lost power, phone lines, and internet access.
The plumes of gas, smoke, and ash erupting from the volcano reached 20 kilometers into the sky, according to Tonga Geological Services.
At 23:55 (14:55 GMT) on Saturday, a 1.2 m tsunami was recorded in the Kominato district of Amami-Oshima Island in Kagoshima Prefecture.
The initial eight-minute eruption was so powerful that it could be heard as "loud thunder sounds" in Fiji, more than 800 kilometers away, according to officials in the capital, Suva.
Japan has warned of waves as high as three meters, and waves of 1.2 meters hit the south of the country.
The US warned of strong currents and waves, and coastal flooding.
The huge underwater volcanic eruption caused waves of more than a meter to crash into Tonga.
The eruption of the Hunga Tonga-Hunga Ha?apai volcano was heard across the South Pacific, and eventually as far away as the US.
Many parts of Tonga, whose capital is just 65 km (40 miles) south of the eruption, are covered in ash and are experiencing a near-total blackout of power, phone lines and internet services. The extent of any injuries or damage is still unclear.
Social media footage showed water washing through a church and several homes, and witnesses said ash was falling over the capital, Nuku'alofa.
Videos on social media showed traffic jams as people tried to flee low-lying areas by car.
One resident, Mere Taufa, said the eruption had hit as her family was preparing for dinner, and her younger brother had thought bombs were exploding nearby.
"My first instinct was to take cover under the table, I grabbed my little sister, and screamed at my parents and others in the house to do the same," New Zealand news site Stuff.co.nz quoted her as saying.
Ms. Taufa said the next thing she knew, water was rushing into their home.
You could just hear screams everywhere, people screaming for safety, for everyone to get to higher ground," she added.
The plumes of gas, smoke and ash pouring from the volcano reached 20 km into the sky, Tonga Geological Services said.
In Japan, the 1.2 m tsunami was recorded in the Kominato district of Amami-Oshima Island in Kagoshima Prefecture at 23:55 (14:55 GMT) on Saturday.
So violent was the initial eight-minute eruption that it could be heard as "loud thunder sounds" in Fiji, more than 800 km away, according to officials in the capital, Suva.
The Fijian government issued a tsunami advisory and opened evacuation centers for people in coastal areas. Vanuatu, another island nation in the Pacific, issued a similar warning.
Prof Shane Cronin, a vulcanologist at the University of Auckland, said the eruption was one of the biggest in Tonga in the past 30 years.
"This is a pretty big event - it's one of the more significant eruptions of the last decade.
"The most remarkable thing about it is how rapidly and violently it's spread. This one was larger, a much wider lateral spread, much more ash was produced. I expect there to be many centimeters of ash that have been deposited on Tonga."
A spokesperson for the Australian government said the prime minister and minister for foreign affairs were monitoring the situation and ready to provide support on request.
A tsunami warning has been issued for parts of Australia's east coast and Tasmania.
In New Zealand, which is more than 2,300 km away from Tonga, the National Emergency Management Agency said coastal areas on the north and east coast of the North Island could see "strong and unusual currents and unpredictable surges at the shore".
Local forecaster Weather Watch tweeted about the eruption: "The energy release is simply astonishing", adding: "Reports of people hearing the sonic booms across New Zealand."
Vanuatu, another Pacific island nation, issued a similar warning.
Prof Shane Cronin, a vulcanologist at the University of Auckland, described the eruption as one of the most powerful in Tonga in the last 30 years.
Parts of Australia's east coast and Tasmania have been issued with a tsunami warning.
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