Incidents of attacks by macaques - a species with reddish-pink faces common across India - are frequent in the city.
"The main door of the house was open and my wife was breastfeeding our son", the 12-day-old baby's father was quoted as saying by The Times of India.
This isn't the first time that a child has been attacked in Agra.
Indian police said a group of the animals entered the boy's home before one of them ran away with him.
"The monkey bit the infant's head and left the baby when people chased it with sticks and threw stones at it", said Ajay Kaushal, the officer in charge of the nearby police station, told the Reuters news agency.
The baby named Sunny was found in a terrace adjacent to his mother, Neha's house and was pronounced dead on arrival to hospital.
In May, two tourists were also attacked while they visited the Taj Mahal.
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The baby's grandmother Pushpa Devi told the station the family would "never recover" from the sudden, shocking loss.
Last month, another man also died as a result of an attack involving a group of monkeys.
"We have registered a case of unnatural death and are getting an autopsy done".
"There is a big monkey menace in the area".
In 2018, the Indian government said it had approved a pilot project for immune-contraception to control the population of wild animals including monkeys in the city.
Environmental activist Shravan Kumar said monkeys are turning more aggressive as their natural habitats have been destroyed and forest cover is gradually vanishing and they go in search of food and shelter. Some local organizations have called for monkeys to be sterilized and excluded from wildlife protection legislation, Singh added.