The incident comes as authorities were beefing up security ahead of the popular emperor's abdication on Tuesday after a 30-year reign.
The man, identified as Kaoru Hasegawa, was arrested on suspicion of illegally entering the premises of the junior high school the 12-year-old prince attends on Friday, public broadcaster NHK and other news reports said.
His motive was not immediately clear.
NHK said police officials were questioning him and suspected he placed the knives at the desk, while Nippon Television said he admitted the allegations.
A police spokesman declined to comment.
Hisahito, who began attending the school this month, was not in the classroom when the knives are believed to have been left.
There were no reports of any injuries or damage at the school, while police did not find any threatening note related to the case.
Security camera footage showed a man with a helmet trespassing on the school grounds at around noon, they said.
Police had been searching for the middle-aged man who was dressed as a construction worker.
Threats to the imperial family are relatively rare. In 1975, Akihito was almost hit by a Molotov cocktail in Okinawa, a major World War II battlefield where there was strong anti-emperor sentiment.
The incident comes as Japan is preparing for the abdication of Akihito, the first monarch to relinquish the throne of the world's oldest imperial family for two centuries.
Akihito's eldest son, 59-year-old Crown Prince Naruhito, will take the throne on Wednesday in a series of ceremonies.
Hisahito is the son of Naruhito's younger brother and the last eligible male heir.
Japan's centuries-old succession would be broken if Hisahito does not have a male child as the Imperial Household Law, in place since 1947, does not allow women to ascend the Chrysanthemum Throne.