The two fingers, including the toe of his right foot, would be amputated in a surgery scheduled for next week, the boy's father said.
Vishal Singh had gone to buy oil for his motorcycle when he had come in contact with the hanging live wire.
Locals have alleged negligence on the part of the power distribution company operating in north-east Delhi's Karawal Nagar area where the incident occurred.
They have also alleged that the discom was informed about the unattended wire but they had not done anything.
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According to Vishal's father, Bhagwan Singh, his son had collapsed on coming contact with the wire and sustained serious burns on his hands and legs.
People present at the spot had rushed him to Guru Teg Bahadur Hospital, where his condition was stated to be stable.
According to the police, angered by the incident, the boy's family had blocked traffic for several hours in the area and demanded action against the discom.