The arrested accused have been identified as Samir Azad (22), Iqbal Khan (21) and Firoz Khan (42), they said.
The victim, identified as Mukesh Yadav, had been abducted on March 20 from a video-game parlour.
Samir Azad, who owned the parlour, and two others kidnapped the boy apparently for ransom, Superintendent of Police (SP) Purshottam Sharma told reporters.
The trio took Mukesh to a closed coal mine in Shivpur area and strangled him with a belt.
According to police, the abductors thought that they would be caught in this case if the boy was released.