Gascón, the first transgender woman nominated for best actress, plays a Mexican cartel boss in the movie, which won a record number of Oscar nominations for a foreign-language film.
The 52-year-old said she hoped "my silence will allow the film to be appreciated for what it is, a beautiful ode to love and difference."
Last week's unearthing of old posts by the Spanish star denigrating Islam and African American George Floyd has unleashed a scandal that has harmed her reputation and the film.
Gascón said she made the decision after the movie's French director Jacques Audiard this week called the posts "inexcusable" and "absolutely hateful".
"I decided, for the film, for Jacques, for the cast, for the incredible crew who deserves it, for the beautiful adventure we all had together, to let the work talk for itself," Gascón wrote on Instagram.
"I sincerely apologise to everyone who has been hurt along the way," added the Spaniard, who was writing in English.
Gascón stars as a drug cartel boss who transitions to life as a woman and turns her back on crime in the highly unusual musical thriller.
The mostly Spanish-language movie filmed in France and set in Mexico was nominated for 13 Oscars, 11 BAFTAs -- Britain's equivalent to the Oscars -- and 12 Cesars in France.
It picked up four Golden Globes in January, including for best comedy or musical, and won multiple prizes at last year's Cannes Film Festival.
Before the scandal broke, Gascón was considered a frontrunner for best actress at the Oscars and pundits viewed the film as a strong contender for the best picture award.
Hollywood trade outlets had reported that distributor Netflix, which was banking on "Emilia Perez" for its first best picture Oscar, had dropped her from its campaign and distanced itself from the best actress nominee.
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