On hearing it's cries, pilgrims alerted police, who took the baby to a police station.
The baby, wearing a shirt and kept in a sleeping bag, was found at around 3 AM, police said.
CCTV footage did not provide any clues, they said.
Though several pilgrims came forward to take the baby, police said they declined the offers and later handed over the child to the government run Shisu Vihar here, police said.