An earthquake with a magnitude of 8.6 has struck under the sea off Indonesia's northern Aceh province.
The Pacific Tsunami Warning Center (PTWC) said a tsunami had been generated but its likely impact was not yet clear.
It advised national authorities across the Indian Ocean region to "take appropriate action".
The region is regularly hit by earthquakes. The Indian Ocean tsunami of 2004 killed 170,000 people in Aceh.
One official quoted by Reuters said a 17cm (6.7in) tsunami had been generated and was heading for the coast of Aceh.
The US Geological Survey (USGS), which documents quakes worldwide, said the Aceh quake was centred 33km (20 miles) under the sea about 495km from Banda Aceh, the provincial capital.
It was initially reported as 8.9 magnitude but was later revised down to 8.6 by the USGS. Strong aftershocks were also reported.
The BBC's Karishma Vaswani in Jakarta says there were reports of the ground shaking for up to five minutes.
'Remain vigilant'
People fled for higher ground in Aceh province
The PTWC alert said quakes of such a magnitude "have the potential to generate a widespread destructive tsunami that can affect coastlines across the entire Indian Ocean basin".
A later alert said that sea level readings indicated a tsunami was generated and that it "may already have been destructive along some coasts".
Indonesian President Susilo Bambang Yudhoyono told reports in the capital that there had been no tsunami reports so far, "but we remain vigilant".
"Our warning system is working well, and I have ordered the national relief team to fly immediately to Aceh to ensure the situation is under control and to take any necessary action," he said.
Bruce Presgrave of the USGS told the BBC that the quake was caused by the earth moving horizontally, rather than vertically, therefore had not displaced large volumes of water.
"We can't rule out the possibility, but horizontal motion is less likely to produce a destructive tsunami," he said.
Sutopo, a spokesman for Indonesia's disaster mitigation agency, said electricty was down in Aceh and there were traffic jams to access higher ground.
"Sirens and Koran recitals from mosques are everywhere," he told Reuters.
'Minute of chaos'The earthquake monitoring agency in Indonesia said the tsunami warning would remain in place for another few hours, but that there had been no reports so far of a low tide, which would indicate the water was receding before building into a tsunami.
The tremor was felt as far away as Singapore, Thailand, Sri Lanka and India.
"There was a tremor felt by all of us working in the building," a man called Vincent in Calcutta, India, told the BBC.
"All just ran out of the building and people were asked not to use the elevator. There was a minute of chaos where all started ringing up to their family and asking about their well-being."
The Thai office of disaster management said people along the coasts of Phuket, Phang Na and Andaman province should heed warnings and evacuate.
Tsunami warning sirens, set up in many vulnerable areas after the 2004 disaster, were heard in Phuket, where correspondents said people were calmly following evacuation routes to safe zones.
Indonesia straddles the Pacific Ring of Fire, a zone of major seismic activity.