The boy was wearing navy shorts, a black pullover and red sneakers, the police said.
They are investigating whether the parents should be charged with abandoning their child.
Members of the public reacted with outrage on social media.
“This is not punishment but abuse!” one Twitter post read.
“The parents are so stupid that I am speechless,” said another.
Many also expressed worry about the fate of the child in the forest alone, apparently with no food or water, as heavy rain hit the area overnight.
Mitsuru Wakayama, a spokesman for the nearby town of Nanae, said local residents pass through the mountainous area only occasionally, when they use it as a shortcut.
“Not many people or cars pass by, and it gets totally dark as there are no lights,” Wakayama said. “It’s not surprising to encounter bears anywhere in the area.”