Kathleen Harkin had been enjoying a night out with friends in Perth when she went missing.
It is understood the group thought the 15-year-old had split-off to walk with other friends and that she was in company.
Police Scotland said it appears this was not the case and that she may have been alone as darkness fell.
The group had made their way to Woody Island – actually part of the riverbank near to North Muirton.
At high tides and when in spate it does become an island but at present is not cut-off.
Kathleen’s mobile telephone was found near to where she was last seen by her friends, at around 9pm.
Police Scotland said Kathleen’s disappearance was “completely out of character”, heightening the concern around her safety.
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Chief Inspector Maggie Pettigrew said: “She is a happy person.
“You can see from the outpouring of comments on social media that she is a well-liked young lady.”
UPDATE (October 10, 17:30): A female body has been retrieved from the River Tay this afternoon. The identity is as yet unknown.