The attack was alleged to have taken place in Worthing in 1970. But Police said the victim was "unwilling to co-operate in any investigation".
Sir Jimmy, who died last year, has been accused of a string of attacks.
Meanwhile, a plaque outside his flat Scarborough has been defaced.
It had been installed in September by a community group set up in memory of the entertainer, but has now been marked with graffiti.
Scarborough Borough Council says it is also reviewing security at Woodlands cemetery where the late DJ and presenter is buried.
The assault revealed by Sussex Police on Wednesday follows similar claims, many of which have surfaced following publicity for an ITV documentary due to be aired this week.
The documentary contains several claims of sexual abuse against Sir Jimmy, from women who were in their teens in the 1970s.
Sussex police said in a statement that a 59-year old woman had reported an assault in March 2008, revealing it had taken place on sometime between May 1970 and September 1970.
"Initial enquiries were made but the woman made it clear at the outset that she was unwilling to co-operate in any investigation or to support any prosecution, and it was therefore not possible to pursue the matter."
The statement continued: "We take all such reports seriously, however long ago the period they relate to, but in this case it was not possible to progress any investigation."
Among the latest women who have come forward with allegations of sexual abuse is Katrina Rose, who was aged 14 in 1975.
She told the BBC she was invited by Savile to see a studio before stopping at his flat to call a cab, which is where she claims the assault took place.
"I froze. I just didn't know what to do. Did not know what was happening. I was quite a naive 14-year-old," said Ms Rose.
"I would feel physically sick even to hear his name spoken. The worst thing that I will never get out of my head is the taste of his cigar breath."
Ms Rose also said in an interview with BBC News that she chose not to pursue a police investigation at the time because she was told:
"You need to be prepared for the media circus it will cause, you will have the press camped on your doorstep. I decided I couldn't cope with that."
She continued: "And, as understandable as that is, I don't think I'll ever stop beating myself up for not having the courage to continue with that and get it out in the open while he was still alive."
Rose has now called for an inquiry into whether Savile was protected by people around him.
"There has to be a full investigation of who knew, who deliberately covered it up. People had to have known something was not right.
"They might not have realised the extent of it. But they had to have known that this man liked young girls just a bit too much."
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