Shinzo Abe, the prime minister, said: "We want to ensure the safety of residents and do our best in rescue efforts."
A 52-year-old woman died in Wajima, on the western side of the peninsula, after being trapped under a stone lantern that toppled over in her garden, officials said.
Media said about 40 people were being treated in the hospital in Wajima.
A hotel employee in Wajima told NHK: "Sprinklers went on, some walls collapsed. It's really bad."
In Nanao, a city with a population of 60,000 on the peninsula, ambulance services were flooded with calls to help people who had burns and other injuries, Kyodo said.
TV footage showed collapsed wooden houses, roof tiles scattered on narrow streets and a man digging through piles of boards from a collapsed house in Wajima.
Some trains were cancelled and people were trapped in lifts as there were power outages in some areas. Flights were suspended between Tokyo and airports in Ishikawa, Kyodo reported.
Shortly after the first quake, a smaller aftershock with a magnitude of 5.3 jolted the same area of Japan, public broadcaster NHK said. However there were no reports of further damage or injuries.
Separately, two earthquakes struck near the island of Vanuatu in the South Pacific, Australia's geological agency reported, but there were no immediate reports of damage.
The first measured 7.3 on the Richter scale and occurred two minutes before the earthquake in Japan. Vanuatu's second, at magnitude 7.1, was about half an hour later.
A tsunami warning for waves of up to 50cm had also been issued for Japan's Ishikawa prefecture. NHK said a small tsunami had hit in some areas causing little damage.