It's considered the country's most dangerous plant because it sits in an area where a major earthquake is expected within the next three decades.
The government issued the request after evaluating the country's 54 reactors for quake and tsunami vulnerability.
Chubu Electric Power Co., the plant's operator, agreed to shut the plant down while it builds a seawall and improves other tsunami defenses there.
Since the March 11 disasters, Chubu Electric drew up safety measures that include building a 40-foot-high seawall nearly a mile long over the next two to three years, company officials said.
Chubu also promised to install more emergency backup generators and other equipment and improve the water tightness of the reactor buildings.
The March 11 quake and tsunami left more than 25,000 people dead or missing on the northeast coast and triggered the worst nuclear crisis since Chernobyl in 1986.
Despite the problems with the Fukushima plant following the disasters, government officials said there are no plans to shut down any other reactors.
At the Fukushima plant Monday, workers and nuclear inspectors briefly entered the No. 1 reactor building to monitor radiation levels, as part of preparations to install a cooling system in the badly damaged unit that had been off-limits for weeks due to high radiation levels.
The Associated Press contributed to this report.