Apple's Beats brand in April unveiled the Powerbeats Pro, a redesigned wire-free version of its popular fitness-oriented Powerbeats earbuds.
Apple Corps Lose Lawsuit Against Apple Computer
Mr Justice Mann ruled iTunes was "a form of electronic shop" and not involved in creating music.
"I conclude that the use of the apple logo ... does not suggest a relevant connection with the creative work," he wrote in his judgment.
According to the BBC, Apple Corps is planning to appeal the case.