The life sized, bronze sculpture of Sandy Irvine Robertson OBE, which can be found at the shore, has been spray painted by vandals.
His hand has been painted bright red with spray paint, and has been flagged to the council, who have pledged to clean it as quick as possible.
Sandy Robertson founded the Scottish Business Achievements Awards Trust.
He was a wine merchant and a charity promoter, and the life sized sculpture of him was commissioned by his friends after his death in 1999.
It was sculpted by Lucy Poett and sits on a bench at the Leith Waterfront.
Group ‘Save Our Shore, Leith’ tweeted a picture of the graffiti to the council asking for it to be cleaned.
They told the Edinburgh Evening News: “There's a place for spray paint but it's not on any part of Leith's heritage.”