A man and a woman in their 50s were confirmed dead in hospital after they were found bleeding at the Tomioka Hachimangu Shinto shrine, a police spokesman said.
Further details, including their identity and information about a suspect, were not available, the spokesman said, adding: “No one has been arrested. The case is still under investigation.”
According to local media, police found a survival knife and a Japanese sword with blood on them near the attack site.
One of the victims was the female chief priest of the shrine, located in a bustling area of the capital, Kyodo News said.
It is believed there was some kind of confrontation among the four who were all associated with the shrine, Kyodo said.
One of those wounded was in serious condition, while the other sustained a minor injury, news reports said.
Japan has one of the lowest rates of violent crime in the developed world, and attacks involving weapons of any kind are unusual.