The former US secretary of state was speaking in London alongside her daughter Chelsea to launch their book - The Book Of Gutsy Women: Favourite Stories Of Courage And Resilience.
In their book they share the stories of the women who have inspired them, and the 16-year-old Swede is among them.
Greta was included in the book one year ago when the mother-daughter duo read about her solitary climate strike in front of Swedish parliament.
“We were so moved by it,” Mrs Clinton said on Sunday night at Southbank Centre’s Royal Festival Hall.
Since then, Greta has sailed across the Atlantic and delivered a powerful speech to the UN about climate change.
“It’s been fascinating to watch how scared a lot of grown up male leaders are of this young 16-year-old girl who speaks up about the threat of climate change,” Mrs Clinton said.
The 2016 US Democratic presidential candidate said the fact Greta is a young woman speaking out is “rattling” the paradigms and “ancient DNA” that still exists in society.
“It is maddening to think how much that still operates,” she said.
Chelsea added that people in the US are attacking Greta because they cannot attack the science around climate change.
“More broadly her real clarity and fearlessness and just being so unbowed and relentlessly focused on the future I think is incredibly threatening to a lot of people,” she said.
Other women in the book include the youngest Nobel Prize laureate Malala Yousafzai, American educator and advocate for the blind and deaf Helen Keller, and professional tennis player Serena Williams.
The book also features other not so well known women such as Diana Nyad who became the first person to swim in waters infested by sharks and lethal jellyfish from Havana, Cuba to Key West, Florida without a protective cage.