Officially known as "Dirty Corner," the 60-metre long, 10-metre high steel-and-rock abstract sculpture has become popularly known as the "queen's vagina".
It is set up in the garden of the chateau, which attracts five million tourists a year.
The phrase "Respect Art as U trust God" was scrawled over the artwork in large letters with pink paint, the management of the palace said yesterday, adding that security at the site would be stepped up with nighttime police patrols and new surveillance cameras.
When it was first unveiled in June the piece was sprayed with yellow paint.
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On Sunday, it was vandalised for a second time when it was covered in anti-Semitic graffiti in white paint.
Phrases such as "Queen sacrificed, twice insulted" and "the second rape of the nation by deviant Jewish activism" covered the work.
Following that incident, the 61-year-old British-Indian artist said he wanted the graffiti to remain to bear witness to hatred.
France's culture ministry agreed, and said panels next to the work would explain what happened.
It is one of several by the artist on exhibition in the gardens and inside one room of the palace until November.
Kapoor's exhibition is one of the most controversial at Versailles since the authorities in 2008 opened the palace and its grounds to contemporary artists.
His work is not the first to raise anger in France.
In October 2014, vandals in Paris's Place Vendome deflated a massive sculpture by American artist Paul McCarthy that was shaped like a sex toy.