The Ukrainian chess grandmaster said the decision to skip the tournament would cost her two world champion titles and a substantial amount of money.
“Exactly one year ago I won these two titles and was about the happiest person in the chess world but this time I feel really bad. I am ready to stand for my principles and skip the event, wherein five days I was expected to earn more than I do in a dozen of events combined," she wrote in a message posted on Facebook.
"Not to play by someone's rules, not to wear abaya, not to be accompanied getting outside, and altogether not to feel myself, a secondary creature."
The prize money for the tournament amounts to a record A$2.61 million.
Anna Muzychuk's sister Mariya is also skipping the event.
The governing body for the World Chess Federation, FIDE, had claimed a win when it successfully lobbied for the authorities to relax its requirements for high-necked white blouses, known as full-body abayas.
The decision to relax the dress code sets a precedent for sporting events held in the country.
The rules for the tournament had stipulated all players to wear trousers and high-necked white blouses, known as full-body abayas. Jeans, T-shirts, baseball caps and shorts had been defined as "inappropriate dress" for the playing zone.
But the tournament, which opened on Monday, has been dogged by controversy with Israel's chess federation saying it is seeking compensation from FIDE after its players were denied visas to compete in the event.
Qatar's chess federation said although its players had been granted visas, they would not be participating because organisers had demanded that the players not display the Qatari flag.
Chess players compete at the King Salman Rapid & Blitz Chess Championships on December 26, 2017 in Riyadh, Saudi Arabia. Source: Getty
Crown prince Mohammed bin Salman has been promoting the country's hosting of the chess event as part of a broader push for social reforms, including the removal of a ban on women driving.
The tournament runs until Saturday, involving 240 men and women from 70 nations.
Saudi law enforces a strict form of Sunni Islam known as Wahhabism.
Women must follow a dress code and must be accompanied, or receive written permission if they wish to travel or work.
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