Wasim Akram was in the kitchen with his mother when the animal snuck inside, pounced on the child and took him deep into the woods, officials said.
Local officials in the northern state of Jammu and Kashmir have sought "elimination orders" from the state government.
It was the third such killing blamed on the leopard in the last two months, including an eight-year-old boy mauled to death in the area on December 7.
In the meantime a team of wildlife officials equipped with tranquiliser guns have been scouring the area to spot the animal.
"The leopard was spotted this morning but we could not trap it," Jammu regional wildlife warden Tahir Ahmad Shawl told AFP.
Wildlife authorities have also issued advice for people in the area to stay safe from animal attacks.
"This is a forested area and humans have entered into their (animals') habitat and not the other way round. Therefore these incidents happen," Shawl said.
Official estimates suggest there are between 12,000 and 14,000 leopards in India.
An estimated 431 leopards were killed in 2017, according to government figures. Most were killed by poachers for their hides and body parts.
Urban expansion has reduced their numbers as forest habitats shrink, bringing them into closer contact -- and conflict -- with humans.
There are no figures on the number of humans killed by leopards, but experts say there are hundreds of deaths each year.
Last week a Buddhist monk was killed by a leopard while meditating in a forest in the western state of Maharashtra, the fifth such attack in the area this month.
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