The actress, 55, was attending a charity auction after a Broadway performance of her former co-star’s new production The Music Man.
Video filmed by Dominique Moreno shows the audience applauding Kidman after she made her bid.
“I can tell you this is not a surprise to me. She is one of the most generous souls I know,” Jackman said.
Posting a photo of the hat on Instagram, Kidman said it was an “honour” to make the donation.
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