She is the first woman to win the £10,000 prize since Laura Solon in 2005.
Christie, in her acceptance speech at a ceremony hosted by Steve Coogan, said she was accepting the award on "behalf of all female comics". She received the reward wearing a "No More Page 3" T-shirt.
The 38-year-old, who has performed at the Fringe for the past 10 years said that normally "nobody had really come" to her shows. She said: "It might mean people will come next year, so it's good that people will know who you are."
Christie said there were some amazing women performing in Edinburgh this year and she was shocked there were not more on the awards shortlist.
There have only been two previous female solo women who have won the prize in its 33-year history - Jenny Eclair in 1995 and Laura Solon in 2005. "I'm in good company," said Christie. "But hopefully that might change. I don't really feel it's about me, it's about women. You had better watch out, we are taking over."
Christie, married to fellow comedian Stewart Lee, praised the high standard of female performers at this year's festival and expressed surprise that there were not more on the awards shortlist.
The six other comedians nominated for the award included Carl Donnelly, James Acaster, Max and Ivan, Mike Wozniak, Nick Helm and Seann Walsh. Coogan, currently starring in the movie Alan Partridge: Alpha Papa, won the comedy prize in 1992, when it was called the Perrier award.
The judging panel saw 578 shows over the three weeks of the Fringe.