Kengo Satake, the boy's 48-year-old father, told police that he "argued with his son for not studying" before a test to enter a private junior high school, public broadcaster NHK reported.
Competition for entry to the best schools in Japan is intense. Admission to a prestigious one is seen as having a decisive impact on a child's future prospects.
The son, named Ryota, was taken to hospital Sunday after the stabbing but died from loss of blood, Aichi prefectural police in the central city of Nagoya told AFP.
"The father stabbed his son in the chest with a kitchen knife," a police spokesman said, declining to provide details of the motive.
The father was arrested after police got a call from hospital staff, he said.
Satake reportedly told police he had stabbed his son "by mistake."
The boy was aiming to enter one of the leading private schools in Aichi prefecture and his father had regularly scolded him over his studies, NHK said, citing people with knowledge of the family.
The boy's mother was at work when the incident occurred, the Asahi Shimbun daily reported.
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