The First Minister and former presidential candidate were both speakers at the Women in the World summit and posed for photos when they met backstage afterwards.
Journalist Tina Brown, who founded the event, also shared a picture of herself with the political “power couple”, calling them “two women I admire most anywhere”, while Ms Sturgeon’s husband, SNP chief executive Peter Murrell, also tweeted a picture of the pair meeting.
Speaking to Ms Brown on stage, Ms Sturgeon said: “I look at Hillary [Clinton] and she has been a trailblazer for women in politics, whatever you think about her politics.
“I find many of her qualities are admirable. Her sheer resilience I find utterly amazing, but she has made it easier for women like me in politics, and I think that I and women across the world really owe Hillary Clinton a debt of gratitude.”
During the interview, Ms Sturgeon also spoke about the Daily Mail’s recent “Legs-it” headline, which ran alongside a picture of her with Prime Minister Theresa May.
“I try not to overreact because I think sometimes papers like the Daily Mail do it to get attention, so why give them what they want... but it’s a vivid illustration of how much more we have to achieve,” she said.
“This tendency to reduce women to body parts or their hair... it’s not innocent and it’s not something we should just laugh off.”
Ms Sturgeon also touched upon the recent decision to go public about her miscarriage in 2011.
“It wasn’t a decision I took lightly, but I decided to speak out about it because it’s one example of a position I’m in to change the attitude toward certain things,” she told the audience.
On being asked why she doesn’t have children, she made the point: “My predecessor didn’t have children, and I’m not aware that he was ever asked that question.”
The SNP leader travelled to the event as part of a US tour which has been criticised by some opponents as a waste of taxpayers’ money.