The Hollywood star, who has landed two Academy Awards for her performances, said her son Raphael damaged the gold covering on the statuette.
Appearing as a guest on tomorrow's edition of The Graham Norton Show on BBC1, she said: "My son was playing with it and all the gold was peeling off - the naked Oscar was getting even more naked.
"It was a very dull and grey colour behind the gold. They replaced it of course but I had to return the old one. I would have liked to keep it - it was cute."
The 50-year-old added: "My son hasn't touched the new one."
French-born Binoche collected the best actress Oscar in 2001 for Chocolat and in 1997 she triumphed as best supporting actress in The English Patient.
The interview is to be screened tomorrow at 10.20pm.