Authorities believe the teenager, whose name has not been revealed, struck her classmate, Aiwa Matsuo, on the head and then strangled her.
The body was discovered Sunday morning, partially dismembered and with several cuts, inside the suspect's apartment where she lives alone.
Following her arrest, the teenager admitted that she was responsible for the murder and explained that she "wanted to try killing someone", police told state channel NHK.
The girl is undergoing psychiatric evaluation, NHK added.
In the teenager's apartment, police found a blood-stained knife, a saw and a hammer presumably used in the crime, which had been acquired by the accused a few days before, in an indication that the murder was premeditated.
The victim and the accused went together shopping Saturday and later to the apartment of the latter where the murder took place.
The victim's parents called authorities after their daughter did not return home Saturday night and police found her body when they went to the apartment to search for her.
Police is also investigating the possible connection of the crime with a series of anonymous messages posted on an internet forum describing an alleged killing as well as several photos containing blood stains.
The messages were posted by the same anonymous user Saturday night, approximately two hours after the murder took place, the Sankei daily reported.
Media also said the minor had been living alone since April in the apartment, where she moved after her mother died due to an illness last year and her father remarried.
The suspect had behavioural problems in the school which both girls attended and police is questioning teachers and fellow students to try and solve the crime, sources related to the case told the Kyodo agency.
The school has also begun to offer counselling to students and has asked them not to discuss the case, the principal said at a press conference Monday.
The incident, which has shaken the city and the Japanese media, is not the first of its kind in the country which has witnessed an increase in crimes by minors since the 1990s.
One of the most shocking cases occurred in 1997 when a 14-year-old boy killed two primary school students in Kobe and sent macabre notes to local newspapers challenging them to expose and arrest him.
Another similar incident took place in Sasebo in 2004 when a high school student killed a classmate because she had criticised her looks in a chat.