Paikidze won the U.S. championship in 2016 and is rated as a Grandmaster by FIDE, the sport's international governing body.
"I'm protesting FIDE's decision not because of Iran's religion or people, but for the government's laws that are restricting my rights as a woman," Paikidze wrote.
Paikidze also created a petition on change.org calling on FIDE to reconsider holding the tournament in Iran and accusing it of violating its own stated principles against sexual discrimination.
FIDE responded to the boycott in a statement.
"There were no complaints from the players or officials and everybody respected the laws of the country, including the dress requirements," FIDE said, referring to three international women's tournaments Iran had recently hosted.
The organization said the dress requirement is Iran's policy, not its own, and that it is "reviewing all possible solutions for the players’ comfort and will discuss all the issues with the organizers in Iran during meetings in the next few weeks."
But Iran's 2015 Asian continental women's champion and grandmaster, Mitra Hejazipour, said Paikidze's decision to boycott would undermine efforts for progress in Iran.
“This is going to be the biggest sporting event women in Iran have ever seen; we haven’t been able to host any world championship in other sporting fields for women in the past,” Hejazipour, 23, told The Guardian newspaper. “It’s not right to call for a boycott. These games are important for women in Iran; it’s an opportunity for us to show our strength."
Iran is known to enforce its hijab law harshly. In May, six young Iranian women were arrested and sentenced last month to a year in prison and 91 lashes after posting a video of themselves dancing without a headscarf. Their sentences have been suspended for three years if they remain out of trouble.