The priestess, named in Japanese media as 58-year-old Nagako Tomioka was on the way to the shrine and was attacked when stepping out of her vehicle. Japanese media said he is the victim's brother, but police would not confirm that.
After attacking his sister, Shigenaga Tomioka apparently killed his female companion and then himself, the police sources added.
Her driver reportedly has also been wounded.
After slashing the priestess, Shigenaga Tomioka then stabbed the younger woman to death with a sword, before killing himself, police said.
Authorities suspect a row between the brother and sister over the shine's chief priest position had prompted the apparent murder-suicide.
The accomplice attacked the driver with a samurai sword and pursued him as he ran out of the temple grounds and about 300 feet down a road, police said.
A blood-stained samurai sword and survival knife were retrieved from the scene.
The almost 400-year-old Tomioka Hachimangu shrine is known for its close ties to sumo and holding one of Tokyo's three big Shinto festivals. The driver's injuries were not life-threatening.
Shigenaga sent a threatening letter to his sister in 2006, saying he would "send her to hell", the Sankei newspaper said.
The shrine dates back to 1627 and is best known for its summer water-splashing festival, seen as one of the top three festivals in Tokyo. The almost 400-year-old shrine is known for its close ties to sumo and holding one of Tokyo's three big Shinto festivals.