Moore, 69, said the women’s game “rides on the coat-tails” of the men – a view described as “sexist” by the United States Tennis Association (USTA).
Women’s world number one Serena Williams said Moore’s statement was “offensive and very inaccurate”.
But her male counterpart, Novak Djokovic, claimed his tour should fight for more money.
Moore said female players “should get down on their knees” in thanks to male counterparts such as Roger Federer and Rafael Nadal. The South African – a former player – later apologised for his “erroneous” remarks.
Tennis legend Martina Navratilova said Moore’s comments were “extremely prejudiced”, adding female players may boycott Indian Wells if Moore stayed.
Djokovic, who won the BNP Paribas Open at Indian Wells on Sunday, described Moore’s remarks as “not politically correct”.
But the 28-year-old Serb suggested men should get more prize money because more people watch their matches.
There has been equal prize money in all four majors – the Australian Open, US Open, French Open and Wimbledon – since 2007, and combined Masters events such as Indian Wells and Miami pay the same to men and women.
In a statement, Indian Wells tournament owner Larry Ellison said: “Ray let me know he has decided to step down from his roles as CEO and tournament director effective immediately. I fully understand his decision.”
Steve Simon, WTA CEO, said: “It is the right decision for him to step down. The BNP Paribas Open has supported the payment of equal prize money to all players since 2009.”