Efforts to restore power to almost 3 million households were underway but it was not clear when supplies would be restored, a company spokesman said.
All trains across the island, which is about the size of Austria, were also halted.
Houses are seen after being destroyed by a landslide after an quake in Atsuma town, Hokkaido, northern Japan.
Roof tiles and water covered floors at Hokkaido's main airport, New Chitose Airport, which would be closed for at least Thursday.
The quake struck as Japan was already dealing with the effects of Typhoon Jebi, the strongest typhoon to hit Japan in 25 years, which killed at least 11 people on Wednesday.
"The electric supply was stopped to Tomari nuclear plant, but it can operate without external electric supply for one week", Chief Cabinet Secretary Yoshihide Suga said.
The utility explained that a coal-fired thermal plant in Atsuma, the largest in Hokkaido, was heavily damaged in the quake.
The US Geological Survey said it struck about 68 kilometres south-east of Sapporo, Hokkaido's main city.
A 6.7-magnitude quake rocked the northern Japanese island of Hokkaido.
The central government set up a crisis management taskforce at the prime minister's Office, Suga said.
Rescue work is underway to search for the missing.. The agency said they pose no tsunami risk.
The government is seeking to restore partial power to some areas as soon as possible once Hokkaido Electric Power Co (9509.T) restarts its Sunagawa coal-fired plant, Seko said.
Farming, tourism and other services are big economic drivers on Hokkaido, which accounts for just 3.6 percent of Japan's GDP, but there is some industry.
The quake was centred near the city of Sapporo on Hokkaido.
NHK showed the moment the quake struck the city of Muroran, with its camera violently shaking and all city lights going black moment later.
Officials have said a "large" number of houses in Atsuma have been hit by the slip.
A series of smaller shocks, including one with a magnitude of 5.4, followed the initial temblor, the Meteorological Agency said.
Additionally, Japan Meteorological Agency officials told NHK that risks of aftershocks are substantial for as long as the next week.
"Our prayers to the people of Japan who were affected by a powerful magnitude 6.7 natural disaster that struck their northern region this morning", Presidential Spokesman Harry Roque said in a statement.
Almost two million people live in Sapporo.
Houses destroyed by the landslide in Atsuma town. At least 123 people were injured in Hokkaido, three of them seriously, according preliminary figures released by the prefectural government.
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