Tsunami waves up to half a metre high "will possibly affect several areas in Indonesia" from early Thursday, according to disaster agency spokesman Sutopo Purwo Nugroho.
Mr Nugroho says the first tsunami waves could arrive at around 5:00am (local time) on Thursday in the eastern region of Papua, and that authorities in 19 provinces of Indonesia had been alerted.
"We are urging the provincial and district governments within these areas to take precautions by urging people to stay away from beaches," he said in a statement.
Other areas that could be affected by the tsunami include parts of the main island of Java, the resort island of Bali, central Sulawesi island, and the Indonesian part of Borneo island, according to Mr Nugroho.
"People must remain calm," he said, adding that no one had so far been evacuated.
The earthquake struck in the Pacific Ocean off Chile late on Tuesday, sending tsunami waves of more than two metres crashing into Chile's northern coast.
At least five people have been killed, tens of thousands have fled and some northern areas of the country have been declared a disaster zone.
Indonesia is frequently hit by earthquakes and is home to scores of active volcanoes, as it sits on the Pacific "Ring of Fire", where tectonic plates collide.
More than 170,000 people were killed in Aceh province on western Sumatra island in 2004 when it was hit by a huge quake-triggered tsunami.
The tsunami also killed thousands in other countries around the Indian Ocean.
However, authorities say there is no threat of tsunami in New Zealand and Australia, south-east of Indonesia and with Pacific coastlines.
The Australian Tsunami Warning Centre says there is "no tsunami threat to Australia", while New Zealand emergency authorities say "the earthquake is unlikely to have caused a tsunami that will pose a threat to New Zealand".
Chile tsunami warning after earthquake
Vehicles and boats lie on the shore after a tsunami hit the northern port of Iquique, April 2, 2014. A major earthquake of 8.2 magnitude struck off the coast of northern Chile on Tuesday, causing at least six deaths and triggering the tsunami. (Reuters: Christian Vivero)
Firefighters work to put out a fire in Iquique, Chile after an earthquake struck off the country's Pacific coast on April 1, 2014. (AFP: Aldo Solimano)
Smashed crockery in a house in Valparaiso, Chile after an earthquake struck off the Pacific coast, triggering a tsunami warning, on April 1, 2014. (Twitter: Santi Contreras)
An energy map from the NOAA National Tsunami Warning Center in the USA shows a forecast of tsunami activity in the Pacific Ocean after an earthquake off Chile on April 1, 2014. (NOAA)
Valparaiso residents wait to evacuate to higher ground after an earthquake struck off the Pacific coast of Chile, causing a tsunami, on April 1, 2014. (Twitter: Gonzalo Galvez)
Locals in Iquique, Chile prepare to head for higher ground after an earthquake caused a tsunami off the Pacific coast of Chile on April 1, 2014. (AFP)
Locals take refuge on a football field in Iquique, Chile after an earthquake struck off the Pacific coast, triggering a tsunami warning on April 1, 2014. (AFP: Aldo Solimano)
Local residents in Talcahuano, Chile, pack their belongings and head to higher ground after an earthquake and tsunami warning on April 1, 2014. (Reuters: Jose Luis Saavedra)
Cars and buses start driving to higher ground in the Chilean coast town of Valparaiso after an earthquake caused a tsunami on April 1, 2014. (Twitter: Pancho Sepulveda)
People rush outside to the streets of Antofagasta in Chile after an earthquake caused a tsunami off the country's Pacific coast on April 1, 2014. (Instagram: Jorge Contreras)
Locals gather outside a hospital in Iquique, Chile after an earthquake struck off the Pacific coast, triggering a tsunami warning on April 1, 2014. (AFP: Francesco Degasperi)
The deserted foreshore in Valparaiso, Chile after an earthquake off the Pacific coast triggered a tsunami warning on April 1, 2014. (Twitter: Santi Contreras)
President declares northern disaster zone
Chilean president Michelle Bachelet has declared parts of northern Chile to be disaster zones, including the regions of Arica, Parinacota and Tarapaca.
"The country has faced these first emergency hours very well," she said.
Ms Bachelet is expected to visit the region in the coming hours, when daylight will reveal the full extent of the damage.
The president has ordered military be sent to affected areas to prevent looting and disorder, but already a government minister has said 300 female inmates have escaped from a prison.
Authorities say a number of those prisoners have been recaptured.
Landslides, blackouts and fires have also been reported.
The earthquake hit shortly before 9:00pm (local time) at a relatively shallow depth of 10 kilometres and was centred 86 kilometres north-west of Iquique in northern Chile.
The first waves struck Chile's northern coast within 45 minutes of the quake, with roads left gridlocked as residents abandoned their coastal homes for higher ground.
Geophysicist Brian Shiro with the Pacific Tsunami Warning Centre described the resulting tsunami as "fairly big".
"The rule of thumb to issue a tsunami in the first place is one metre. So this is more than twice that," he said.
Interior minister Rodrigo Penalillo says the victims were four men and a woman who died in the cities of Iquique and Alto Hospicio, either of a heart attack or after being crushed by debris.
Tens of thousands heed evacuation warning
Shortly after the earthquake struck, tsunami warning sirens blared along Chile's coastline, urging people to head to higher ground.
Tens of thousands heeded the call, evacuating their homes and grid-locking roads with heavy congestion.
Freelance journalist Tom Asapati told the ABC from Santiago that authorities wasted no time issuing the warning.
"People have moved out of the danger areas as quickly as they can and now they're waiting for the authorities to give the all-clear so they can go back to their homes," he said.
Coordinator with the Chilean Red Cross Leticia Escamilla said evacuations were relatively calm.
"People who have experienced past earthquakes ... have reported feeling more prepared and have shown actions where they are more prepared," she said.
"This is a very seismic country, so people are always kind of alert. People do seem more prepared and knowing what to do this time around."
Hostel owner Kurt Hertramph said guests at his Arica hostel evacuated to higher ground.
"Everybody's gone, everybody's gone. Mostly they are Dutch, and there is a couple from Australia," he said.
"Everybody's out in the hills in this moment. We got an evacuation plan for that. It's running good at the moment and the police are in the area."
Northern Chile has felt a number of aftershocks since the massive earthquake struck.
Kevin McCue from the Australian Seismological Centre says the aftershocks could go on for months and could be as strong as magnitude 7.
Earthquakes are a common occurrence in Chile. In 2010 an 8.8-magnitude earthquake killed more than 300 people.
Fact file: Earthquakes and tsunamis
- About 80% of tsunamis are caused by an earthquake at or below the seafloor.
- Earthquake causes a large area of the seafloor to either lift up or drop down.
- The ocean water above the displaced seafloor then rises or falls abruptly. This results in a tsunami wave on the surface of the ocean which travels out in all directions.
- The upthrust or downthrust of the ocean bottom can occur over hundreds of square kilometres. This pushes up the water above creating a huge mass of water like a hill.
- As the wave approaches shallow water the front of the wave slows down. The height of the water behind increases as it tries to catch up and leads to the wave breaking
Source: ABC Science