A knife and a Japanese sword with blood on were found later near the site. The sister's chauffeur was also attacked.
Authorities suspect a row between the brother and sister over the shine's chief priest position had prompted the apparent murder-suicide.
Shigenaga and the other woman, who was his girlfriend and believed to be in her 30s, apparently ambushed Nagako after she got out of a auto on the grounds of the shrine in Tokyo's eastern ward of Koto.
The four were sent to a hospital, where the three were confirmed dead.
A woman aged in her 30s who was with Shigenaga Tomioka attacked and stabbed the driver of the vehicle with a Japanese sword, police said. However, he was pursued over a distance of about 100 meters by Shigenaga's girlfriend, who was wielding the Japanese sword. At a spot about 100 meters away from the auto, she slashed his right shoulder, leaving him with a non-life-threatening injury.
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Police said the attacks had been captured by nearby security cameras and that two survival knives and two Japanese swords had been left at the scene.
After slashing the priestess, Shigenaga Tomioka then stabbed a younger woman he was with to death with a sword, before killing himself, police said.
The newspaper reports: "Shigenaga Tomioka was arrested some 10 years ago for blackmailing his sister".
Shigenaga Tomioka, 56, is suspected of having attacked his 58-year-old sister Nagako Tomioka, the chief priest of the Tomioka Hachimangu shrine, the Metropolitan Police Department said.
The attacker and his sister belong to a family that has managed the Tomioka Hachimangu Shrine for generations since its founding in 1627. It is known as the birthplace of sumo. The shrine left the association on September 28 this year.