CBeebies, the BBC's children's channel, ran an episode of "The Tweenies" in which a character appeared dressed as Savile, who police say sexually abused hundreds of people over the course of his 60 years in entertainment, the BBC reported.
The episode was filmed in 2001, the BBC said.
The character Max appeared in a blond wig, using Savile's accent and catchphrases and wearing his style of tracksuits.
"This morning CBeebies broadcast a repeat of an episode of the Tweenies, originally made in 2001, featuring a character dressed as a DJ impersonating Jimmy Savile. This program will not be repeated and we are very sorry for any offense caused," the BBC said.
Savile, who died in 2011 at age 84, allegedly was a "prolific, predatory sex offender" who abused more than 200 people, a police report said.