In a statement this week, US attorney Willie Gary said the suit named HP and its subsidiary Palm, for marketing the software application without permission.
The suit filed a Florida federal court seeks $US500 million ($483m) in damages.
According to Gary, it alleges the app "adversely affects Chubby Checker's brand and value... and will tarnish his image that he has worked to maintain over the last 50 years".
"This lawsuit is about preserving the integrity and legacy of a man who has spent years working hard at his musical craft and has earned the position of one of the greatest musical entertainers of all time," said Gary.
"We cannot sit idly and watch as technology giants or anyone else exploits the name or likeness of an innocent person with the goal of making millions of dollars," he added.
The "Chubby Checker" app, which appears on websites for Palm devices, claims to allow a person to determine a man's penis size by using his shoe size.
Checker, 71, is best known for his 1960 hit "The Twist" which spawned a dance craze during the decade that followed.