The 60-metre (200-foot) long, 10-metre (33-foot) high steel-and-rock abstract sculpture, resembling a funnel in the form of an orifice, is set up in the garden aimed directly at the royal chateau, which attracts five million tourists a year.
Kapoor, 61, has titled the work "Dirty Corner". It is part of an exhibition of his work in the grounds of the 17th century palace that opens on Tuesday and runs until November.
"Anish Kapoor provokes a scandal," said the website of radio station Europe 1.
The conservative daily Le Figaro saw the work as an effort "to use Versailles as an object of contrast between two types of art": the contemporary style of Kapoor and the centuries-old elegance of the French court.
Others came running to the artist's defence. Les Inrocks, a youth pop culture magazine, said only a "fascist" circle of commentators was against the sculpture.