Japanese television showed cars, ships and even buildings being swept away by a vast wall of water after the 8.9-magnitude earthquake.
The quake has sparked fires in several areas including Tokyo. At least 32 people were killed, officials said.
It struck about 250 miles (400km) from the capital at a depth of 20 miles. There have been powerful aftershocks.
The tremor, measured at 8.9 by the US Geological Survey, hit at 1446 local time (0546 GMT). Seismologists say it is one of the largest earthquakes to hit Japan for many years.
Roland Buerk BBC News, Tokyo
When the earthquake hit, buildings in Tokyo swayed. Walking was like crossing the deck of a ship at sea.
People poured down from their offices and stood in the street staring up.
A large fire seemed to have broken out in one part of the city and, in another place, injured people were being brought out of a station.
The authorities immediately issued a tsunami warning.
In Tokyo, public transport has been suspended, elevators are switched off in many buildings and thousands of people have gathered in squares and around train stations.
A tsunami warning was extended across the Pacific to New Zealand in the south and North and South America to the east.
The Red Cross in Geneva warned that the tsunami waves could be higher than some Pacific islands, Reuters news agency said.
Coastal areas in the Philippines, Hawaii and other Pacific islands were evacuated ahead of the tsunami’s expected arrival.
Wall of water
Strong waves hit Japan’s Miyagi and Fukushima prefectures, officials said, damaging dozens of coastal communities. Kyodo news agency said a 10-metre wave (33ft) struck the port of Sendai in Miyagi prefecture.
Japan’s NHK television showed a massive surge of debris-filled water sweeping away buildings, cars and ships and reaching far inland.
Motorists could be seen trying to speed away from the wall of
Farmland around Sendai was submerged and the waves pushed cars across the runway of the city’s airport. Fires broke out in the city’s centre.
Another fire was reported to be burning in the turbine building of the Onagawa nuclear plant in Miyagi prefecture.
The UN’s nuclear agency said four nuclear power plants had shut down safely. Prime Minister Naoto Kan said there had been no radiation leaks.
Police and local officials said at least 32 people had been killed in the earthquake and tsunami. It is believed the death toll could rise significantly.
In Iwate prefecture, also near the epicentre, an official said it was difficult to gauge the extent of the destruction.
“Roads were badly damaged and cut off as [the] tsunami washed away debris, cars and many other things,” said Hiroshi Sato, a disaster management official in Iwate.
The earthquake also triggered a massive blaze at an oil refinery in Ichihara city in Chiba prefecture near Tokyo, engulfing storage tanks.
There were reports of about 20 people injured in Tokyo after the roof of a hall collapsed on to a graduation ceremony.
Residents and workers in Tokyo rushed out of apartment buildings and office blocks and gathered in parks and open spaces as aftershocks continued to hit.
Many people in Tokyo said they had never felt such a powerful earthquake.
In central Tokyo, Jeffrey Balanag said he was stuck in his office in the Shiodome Sumitomo building because the elevators had stopped working.
“There’s no panic but we’re almost seasick from the constant rolling of the building,” he told the BBC.