A circular gold plaque displayed in Scarborough as a memorial to Sir Jimmy, who had a home in the town, has been subject to a graffiti attack with the words "rapist" and "paedophile"
Authorities in North Yorkshire say they are reviewing security at the cemetery where his headstone was placed, following his death at the age of 84 last year.
A statue of the star has also been taken down in Glasgow.
Jimmy Savile was questioned as a suspect by police investigating the Yorkshire Ripper, according to a retired police officer.
Jimmy Savile's nephew has spoken of the emotional turmoil his family is going through in the wake of the sex abuse allegations.
A colleague of Jimmy Savile allegedly raped a woman on BBC premises in 1970, ITV News has been told.