Police sub-inspector Gaje Singh told The Associated Press that the attacks started late Saturday in the Shastri Park area of New Delhi, adding that it was not immediately possible to give an exact tally of the injured. Local news reports said as many as 25 people were injured.
Singh said officers were patrolling the neighborhood in search of the rogue animal.
"But the monkey hasn't been spotted yet," Singh said.
People in Shastri Park often sleep outside their homes or on open roofs to escape the heat.
Neighborhood resident Naseema, who goes by one name, carried her 1-year-old daughter into her house in attempts to escape the animal. "The monkey followed me in and buried its teeth in my baby's leg," she told the Times of India newspaper.
As New Delhi 's forest cover shrinks, rhesus macaque monkeys have overrun its government buildings, temples and residential areas, occasionally biting passers-by or snatching food from them. A government official died last month when he fell from his balcony during an attack by wild monkeys.
Part of the problem is that devout Hindus believe monkeys are manifestations of the god Hanuman and feed them bananas and peanuts, encouraging them to frequent public places.
Last year, the Delhi High Court reprimanded city authorities for not doing enough to stop the animals from terrifying residents.
City authorities have experimented with using langurs - a larger and fiercer kind of monkey - to scare or catch the macaques, but the problem persists.
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