Vasudeo S Gaitonde's untitled painting from 1995 was bought by an anonymous buyer, the auction house said.
The previous record was $4.01m for a work by Goan artist Francis Newton Souza.
Gaitonde, who died in 2001, is considered one of India's greatest abstract painters.
"It achieved a world record for any Indian work of art sold at auction," Christie's International Head of World Art William Robinson said.
The auction on Tuesday was the third for Christie's in India.
An oil painting by an Indian artist has sold for 293m rupees ($4.4m; £2.9m) at a Christie's auction in Mumbai, setting a new world record for Indian art.