The figure had been unveiled at Pollok Country Park in 1993 before being installed at the children's swimming pool at Scotstoun Leisure Centre.
A spokesman for operator Glasgow Life said: "Given the current controversy and the seriousness of the allegations, we thought it appropriate to move the statue at this time."
Savile, who died last year at the age of 84, has been the subject of several allegations that he sexually abused teenage girls.
The statue was removed in Glasgow before last night's documentary Exposure - the other side of Jimmy Savile aired on ITV and STV.
Surrey Police confirmed earlier this week that Savile had been questioned in 2007 on suspicion of alleged offences dating to the 1970s.
The BBC has denied claims of a cover-up over the allegations, claiming a planned Newsnight show had been dropped due to the CPS choosing not to prosecute and the difficulty in proving institutional failure.
It later emerged that controller of BBC Radio 1 and Radio 2 in 1972 Douglas Muggeridge was aware of the allegations and asked them to be investigated by former BBC press officer Rodney Collins.
Jimmy Savile in pictures:
Copyright: flickr/BBC Pictures