Police said the discovery was made at the Port Edgar marina, near South Queensferry town centre, at 8.30pm on Thursday.
A formal identification is expected to take place later today.
Hutchison, 36, was reported missing on Wednesday. He was last seen leaving the Dakota Hotel, close to the Forth Road Bridge, shortly after 1am.
A police search was launched, concentrating on South Queensfery, the bridge, and across the water in Fife.
The popular singer-songwriter achieved critical success as the frontman of Frightened Rabbit, an indie-rock band originally from Selkirk and later based in Glasgow.
The group have released five studio albums to date, with the last two cracking the UK Top 20. They were signed to major label Atlantic Records in 2010.
Mr Hutchison’s family had raised concerns after tweets were sent by Scott shortly before he was last seen.
At about 23:00 on Tuesday, he wrote: “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.”
Minutes later he added: “I’m away now. Thanks.”