The 36-year-old had been reported missing in the early hours of Wednesday – last seen on CCTV footage leaving a hotel.
Police last night discovered a body near South Queensferry about 8.30pm in the search for the singer.
Formal identification is yet to take place but Mr Hutchison's family have been informed, BBC reported.
The Scottish rock star had disappeared after leaving the Dakota Hotel in South Queensferry, Scotland on Wednesday, May 9.
He had previously shared tweets before his disappearance, writing: "Be so good to everyone you love. It's not a given. I'm so annoyed that it's not. I didn't live by that standard and it kills me. Please, hug your loved ones."
His band had tweeted asking fans to look out for the singer.
Frightened Rabbit had only recently announced their first headline festival, First Incident in Glasgow.
Scottish Police had launched a search for Scott and posted appeals for his whereabouts on social media.
Inspector Graeme Dignan from Edinburgh police said: "We are keen to locate Scott as soon as possible to ensure he is safe and well and would urge anyone who can assist with our ongoing inquiries to come forward."
Scott was last seen wearing a dark baseball cap, navy blue hooded jacket, grey or white khaki trousers and white trainers.
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