Dubbed the "queen's vagina", the controversial steel funnel and the rocks around it were sprayed with phrases such as "SS blood sacrifice" and "the second RAPE of the nation by DEVIANT JEWISH activism" at the weekend.
The sculpture had already been attacked in June and then cleaned, but Kapoor said that this time he wanted the graffiti to remain to bear witness to hatred.
France's culture ministry agreed late Monday, and said panels next to the work would explain what happened.
"The work was very seriously defaced, those responsible will be punished."
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The steel-and-rock sculpture, which faces the former royal chateau in its world-famous gardens, is 60 metres (200 feet) long and 10 metres (33 feet) high.
Shortly after the sculpture was unveiled in June, vandals splattered it with yellow paint.
But the 61-year-old British-Indian artist told the daily Le Figaro he would not restore the work as he did the first time, and instead would keep the "abominable words" as part of the sculpture.
"From now on, in the name of our universal principles, these abominable words will become part of my work, they will overlay it and stigmatise it."
The sculpture is one of several by Kapoor which are on show in the gardens and inside one room of the palace until November.
Kapoor has previously described the piece as "the vagina of a queen who is taking power" but later appeared to step back from this description.
Kapoor's work is not the first to spark anger in France.
In October 2014, vandals deflated a massive sculpture by American artist Paul McCarthy that was shaped like a sex toy at Paris's Place Vendome.