The BBC has received 216 complaints about an episode of The Tweenies, in which a character appeared dressed as disgraced TV presenter Jimmy Savile.
The programme, which was filmed in 2001, was shown on CBeebies before 09:00 GMT on Sunday.
In the scene, the character Max appeared in a blonde wig, wearing Savile's trademark tracksuits and using his accent and catchphrases.
Thirty-four people also contacted the BBC to comment on the programme.
A spokesperson for the BBC said the majority of the complaints were made immediately after the programme was broadcast.
Police say DJ and presenter Savile sexually abused hundreds of people during 60 years in entertainment.
Apologising for the sketch, the BBC said: "This morning CBeebies broadcast a repeat of an episode of the Tweenies, originally made in 2001, featuring a character dressed as a DJ impersonating Jimmy Savile.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 programme will not be repeated and we are very sorry for any offence caused."
Media watchdog Ofcom said it was assessing whether any broadcasting rules have been broken, but was not currently investigating.
It is understood that the regulator received "tens, rather than hundreds" of complaints about the episode.
The episode featured the character Max presenting a Top Of The Pops-style programme. He was wearing a wig and used Savile's familiar catchphrase: "Now then, guys and gals."
The gaffe was picked up by fans on social networking sites such as Twitter.
Glenn Ebrey tweeted: "Dear CBeebies, I'm not sure this was a good choice of DJ to impersonate on The Tweenies today."
Kenny Senior wrote "Are BBC trying to self destruct? Max from Tweenies dressed as Jimmy Savile just now nearly chokes on my cornflakes."
A recent Metropolitan police report into allegations of sexual abuse against Savile, who died in 2011 aged 84, concluded the presenter and DJ was a "prolific, predatory sex offender" who abused more than 200 people over a 60-year period.
The Tweenies, which was a co-production between Tell-Tale Productions and the BBC was cancelled in 2003 but episodes have been repeated regularly since then.
Episodes mixed stories, song and creative activities aimed at helping children to learn through play.