The two-year-old female tiger was initially captured in July after killing two villagers and injuring four others in Brahmapuri in Maharashtra state.
It was later released into the nearby Bor Wildlife Sanctuary but went on to attack and kill another two people. Its latest victim, a woman, died earlier this week.
Rishikesh Ranjan, field director of Pench Tiger Reserve, close to Bor, told AFP that a local court had approved a shoot-to-kill order against the tigress, named "Kala".
"She has killed four people and injured four others. We can shoot her but we would prefer to capture and tranquillize her," he said late Thursday.
Ranjan said officials were tracking the tiger using GPS and wanted to catch her as soon as possible because she is "spreading panic amongst villagers".
"In her last killing she consumed a major chunk of the victim's body," he said.
Tigers do not generally attack humans, but some experts believe they can get a taste for human flesh once they have attacked once.
India is home to more than half of the world's tiger population with some 2,226 of the animals roaming its reserves, according to the last count in 2014.
Dozens die every year, sometimes at the hands of poachers, while reports of man-animal conflict are not uncommon. Wildlife activists say they occur when humans encroach into tiger corridors.
In October last year armed forest guards shot dead a man-eating tiger in northern India.
It was blamed for killing three villagers, including a woman outside Jim Corbett National Park in Uttarakhand state.
Villagers celebrated by parading with the dead animal's carcass for nearly three hours.
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