Forensic officers were combing the popular tourist attraction for clues from early morning.
A Police Scotland spokeswoman said: “Police in Edinburgh are investigating a report of a sexual assault in the city centre area.
“The incident was reported at around 6.35 am in the Calton Hill area on Wednesday 03 October. Inquiries are ongoing.”
Anyone with information can contact police via 101 or Crimestoppers aononymously on 0800 555 111.
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