Known as Stopashlee.com, the site was getting about 1,000 signatures per hour, the New York Daily News reported Wednesday.
It is addressed to Geffen Records, Simpson's label, and JT Entertainment, her father's management company.
"We, the undersigned, are disgusted with Ashlee Simpson's horrible singing and hereby ask her to stop," the online petition begins.
The site was created by Bethany Decker, an 18-year-old Staten Islander.
A Simpson spokesman dismissed, albeit courteously, the criticism.
"Ashlee cares deeply about the opinions of all her fans," the publicist said. "But the fact is her album has sold 3.5 million copies, her concert tour is selling out ... her single 'La La' is climbing (on) radio, and the new season of her hit MTV show debuts next week."
Notable deaths of 2014 [PHOTOS]