The app, which was called "The Chubby Checker," was an unauthorized use of Checker's name and trademark, the lawsuit alleges.
"He's hurt," said Checker's attorney Willie Gary. "He worked hard to build his name and reputation over the years."
The app is no longer available.
Checker, who is 71 and lives in Pennsylvania, is seeking a half-billion dollars in damages and restitution.
HP issued a brief statement about the matter on Thursday.
"The application was removed in September 2012 and is no longer on any Palm or HP hosted web site," wrote Michael Thacker, HP's director of corporate media relations.
He told The Associated Press that the app was removed the same month that Gary sent a cease-and-desist letter to the companies on behalf of Checker.
It's unclear how long the 99-cent app was available to customers.
According to the industry website WebOSNation, the app sold fewer than 100 copies.
The app was not developed by HP or Palm; it was developed by a third-party. The app developer is not named in the lawsuit.
"We're going straight to the source," said Gary.
According to court documents, the lawsuit was filed in Florida because HP and Palm do business in the state.
Checker did not give permission or receive compensation from the app, which purported to be for entertainment purposes only.
The lawsuit said that Checker has received patents and trademark licenses for his name to be used for a line of snacks and other food products.
Checker's song, "The Twist" was at the top of the Billboard charts for 18 weeks in 1960 and became an iconic tune of the era.