The Oscar-winning star, 55, made the eye-watering bid for Jackman’s prop from his musical The Music Man at the Broadway Cares/Equity Fights Aids charity event at the Winter Garden Theatre in New York on Saturday.
In a clip from the event which Jackman posted on social media, he and co-star Nicholas Ward asked the audience to beat the top bid of $19,000 (£16,000).
As they upped the bidding ante, Kidman shouted “$100,000 (£83,000)”. She then walked to the stage in a black trouser suit and greeted her stunned friend to rapturous applause.
“Nic! I just want to be clear, this is not Australian dollars,” an astonished Jackman quipped.
Picking up the straw boater, the Hours star gave the 54-year-old a hug and said: “I love you, I love Broadway, and I love what they do at Broadway Cares.”
After the event, Jackman, who starred in the 2008 film Australia with Kidman, said: “I’ve known Nic for almost 30 years.
“I’ve worked with her, I can tell you this is not a surprise. She’s one of the most generous souls I know.
“The generosity and love emanating from Nicole Kidman leaves me speechless. Thank you Nic for your friendship and support.”
Jackman echoed these sentiments on Twitter.
He tweeted: “The generosity emanating from #NicoleKidman leaves me speechless! You ARE amazing.
“Thank you for your friendship and support! @MusicManBway @NicholastheWard @BCEFA”.
And it wasn’t just the Wolverine actor who was left in awe by her kindness, with many of Jackman’s Twitter followers also praising Kidman.
One wrote: “I’ve watched this with a smile on my face and a tear in my eye a dozen times and I still have no idea what organization she is donating the money to!!
“And that doesn’t even matter, her generosity and sincerity are beautiful”.
Another user commented: “I just had to watch this about a dozen times, it's so amazing! Thank you, Nicole, I'm also speechless! I'm crying tears of joy and gratitude. Also, Hugh's face is absolutely priceless.”
A third person added: “What she did is just incredible. Such a generous soul. It's also incredible how much you guys are raising for such an amazing cause. I take my hat off to you all.”