The Chubby Checker app - which appeared on websites for Palm OS devices - claimed to guess the intimate measurement based on shoe size.
Lawyers acting for the singer are seeking $500m (£323m) in compensation, saying the app has done "irreparable damage" to his reputation.
HP said it removed the app as soon as it received a complaint from lawyers.
Lawyers for the 71-year-old singer - real name Ernest Evans - filed a "cease and desist" order against HP and its subsidiary Palm in September 2012, soon after the app became available.
Now they have launched a trademark infringement case against the two tech firms.
Chart topper"He's hurt," his lawyer Willie Gary told Associated Press.
"He worked hard to build his name and reputation over the years.
"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."
The app had used his client's name and trademark without permission, said Mr Gary,
In a statement, an HP spokesman said: "The application was removed in September 2012 and is no longer on any Palm or HP-hosted website."
The German firm behind the offending program, Magic Apps, is no longer selling the software.
It is not clear how many copies it sold before HP and Palm but WebOSNation, which monitors the use of Palm smartphones, estimates it was downloaded only 84 times before it was pulled.
Chubby Checker is best known for his song The Twist which topped the US singles chart in both 1960 and 1962.
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