The 27-year-old Muzychuk is refusing to defend her titles in rapid and blitz chess in Riyadh in protest at the host country's record on women's rights.
Rules governing women's status meant she would have been made to feel "a secondary creature", she said in a Facebook post.
Muzychuk, speaking to Reuters in her home town of Lviv, said she made the decision knowing she would relinquish both her titles and earnings from taking part. Her younger sister Mariya, a former women's world chess champion, would also stay away from Riyadh.
"As to whether it was right or wrong, there will certainly be people who will support me and people who will condemn me," Muzychuk said. "But I took this decision and I am responsible for it."
Saudi Arabia ended a ban on women driving in September but the conservative kingdom's male guardianship system requires women to have a male relative's approval for decisions on issues like education, employment, marriage and travel plans.
More than 200 players from 70 countries are participating in the World Rapid and Blitz Chess Championships, which bear the name of King Salman bin Abdulaziz.
In what the World Chess Federation (FIDE) called an "historic agreement", Saudi Arabia relaxed its dress code for the tournament, which has a total prize pot of $2 million.
This meant women would not need to wear the hijab or abaya -- the loose-fitting, full-length robes that women are typically expected to wear. Instead, inside the venue, women could wear dark formal trouser suits and high-necked white blouses.
But these changes did not go far enough for Muzychuk.
"I have refused to go," she said.
"It was certainly quite difficult to take such a decision because I am a current world champion in these chess disciplines – rapid chess and blitz. So if I do not participate in this tournament, I will lose both titles."
More controversy has dogged the tournament as seven Israelis have been denied visas to participate, a FIDE vice president said. It would have marked the first time Saudi Arabia had publicly hosted Israelis as the Gulf state does not recognise Israel and there are no formal ties between them.
(Editing by Matthias Williams and Richard Balmforth)
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