The move signals a potential shift in energy policy after the Fukushima Daichi plant in Japan's northeast was wrecked by a giant tsunami triggered by one of the biggest earthquakes ever recorded on March 11.
The company said it could restart the plant once its tsunami wall and other safety steps had been approved by the authorities.
That could take two years, raising the risk of a shortage of electricity after the Fukushima plant was shut down by the tsunami.
Compounding public concern over an industry that supplies about 30% of the quake-prone country's electricity, another power operator said it had discovered a tiny amount of leaked radiation at its Tsuruga plant on the west coast.
Japan Atomic Power said it had stopped the leak and that there had been no impact on the environment.
"By halting the Hamaoka nuclear plant, we are causing great short-term trouble to not only those in the plant area but also many others including our customers and our shareholders," Chubu Electric President Akihisa Mizuno told a news conference.
"But firmly implementing measures to strengthen safety would become the cornerstone to continue safe and stable nuclear power in the long-term and in the end lead to the benefit of our customers."
The government is under heavy pressure to review its energy policy, of which atomic power is a major part, after the March quake and tsunami wrecked the Fukushima nuclear power plant run by Tokyo Electric Power .
Nearly 26,000 people were killed or are unaccounted for following the natural disaster which triggered the world's biggest nuclear crisis since Chernobyl in 1986. The plant is still leaking radiation.
Government experts put the chance of a magnitude 8.0 quake hitting the Hamaoka area in the next 30 years at 87%, which has raised questions over why it was built there in the first place.
Trade Minister Banri Kaieda said the government would consider steps to shoulder the cost of closing the plant if requested by Chubu.
The company's shares were down 11% at 1,570 yen in afternoon trade, after falling as low as 1,521 yen. Chubu's tumble helped push Tokyo's electric and gas subindex down 2.7%
"This news is triggering uncertainty not just about Chubu Electric but the whole utility sector," said Yoshinori Nagano, a senior strategist at Daiwa Asset Management.
"Investors are concerned that on the back of this news other reactors currently under inspection may not resume operations soon."
Kan, under fire for his response to the crisis in northeast Japan after the March quake, said the government would try to prevent the halt of the Hamaoka reactors from causing power supply problems.
Chubu has said it can meet peak demand of 25,600 MW even if Hamaoka shuts. But relying on thermal plants to fill the power gap would push up costs by 700 million yen a day - or about 256 billion yen a year, double its projected profit of 130 billion yen in the year to March 2012.
However, an unusually hot summer would raise the risk of Chubu not having enough capacity to meet peak demand, which could cause problems for Toyota Motor Corp and other major manufacturers with factories in the region.
Chubu generates a relatively small proportion of its power from nuclear plants, accounting for 14% of the firm's total electricity generated in 2009/10. That was below a 30% average nationwide, while gas thermal power held a 47% share.