The 51-year-old, who principally rides for Middleham trainers Mark and Charlie Johnston, was unseated by Jim Goldie's Braes Of Doune when he ducked left during the one mile one furlong race.
Fanning, who won the Gold Cup at Ascot last season on Subjectivist, has a fractured humerus which can taken between six to eight weeks to fully recover from, meaning he will miss the busiest period of the season.
Fanning saw a specialist on Friday and his agent Niall Hannity said: "It's not good news I'm afraid, he's fractured his humerus, the bone in his upper arm.
"He went to see a surgeon in York called Simon Boyle who confirmed it.
"He'll be on the sidelines for a while, how long I'm not really sure. He's going back to see the surgeon on Monday, Simon is brilliant with him and he's told him to keep going back to see him.
"He doesn't think they'll need to operate, but it's the worst time of year to happen."