Glitter, whose real name is Paul Gadd, was photographed leaving Charing Cross police station on Sunday afternoon.
Scotland Yard later said Glitter was bailed to return to the police station in mid-December pending further inquiries.
Police did not say what led to his arrest.
The late TV presenter Savile, who died last year at the age of 84, has been described as one of the most prolific sex offenders in recent UK history. Scotland Yard detectives are dealing with about 300 alleged victims and are following more than 400 lines of inquiry.
It has also emerged that Savile's cottage in Scotland was vandalised overnight.
A police spokesman said "abusive slogans'' were painted on the walls of the property.
Officers appealed for anyone with information to contact them. Earlier this week officers searched the cottage to look for "any evidence of any others being involved in any offending with him''.
Glitter's arrest came as the chairman of the BBC Trust, Chris Patten, said he was dedicated to finding out the truth about the scandal that has engulfed the corporation, vowing there would be "no covering our backs''.
Writing in the Mail on Sunday newspaper he said the BBC's reputation was on the line, and that it has risked squandering the public's trust.
Speaking of Savile's apparent decades of criminality, he wrote: "Can it really be the case that no one knew what he was doing? Did some turn a blind eye to criminality? Did some prefer not to follow up their suspicions because of this criminal's popularity and place in the schedules? Were reports of criminality put aside or buried?
"Even those of us who were not there at the time are inheritors of the shame.''
He also apologised "unreservedly'' to the abused women who spoke to the BBC's Newsnight program but did not have their stories told when the report was axed.
The BBC chairman said the two independent inquiries that have been set up - one into the Newsnight report, the other into the BBC's culture and practices in the years Savile worked there - must get to the truth of what happened.
"Now my immediate priority is to get to the bottom of the Savile scandal and to make any and every change necessary in the BBC to learn the lessons from our independent investigations,'' he said.
- AAP
