SS Bhagat and Sachin Mittal, both employed with the hospital, have been arrested, police said.
According to the police, Dev Sharma was admitted to the hospital in Vaishali on Sunday after he complained of pain in a finger.
"The victim's father alleged that the doctors suggested an operation. But after the operation, Dev again complained about the pain. Following this, the doctors gave him three doses of injection and shifted him to ventilator. However, within an hour, they declared the child dead," said a senior police official.