The president of the body that administers the world-famous French monument, Catherine Pégard, declared herself "shocked and saddened" after staff discovered the graffiti at 6.30am Sunday.
Scrawled in white paint on stones at the head of the 60-metre-long steel tunnel, the slogans read "The queen sacrificed, twice insulted", "SS Bloody Sacrifice" and "The second RAPE of the nation by DEVIANT JEWISH activism" (capitals in the original).
Staff were designated to explain to the thousands of tourists who visit the château's park every day that the slogans were not part of the work.
Kapoor has said that the work, officially called Dirty Corner, is "very sexual" and himself coined its nickname.
Far-right and Catholic fundamentalist bloggers were outraged when it went on show at the former royal palace in June and it has already been vandalised once.
"I am scandalised that someone has attacked with the most abominable references the work of an internationally renowned artist and, on top of that, the Château de Versailles and culture," Pégard said Sunday.