Doctor Alan Farrell told the team's official website: "After the crash Edvald was taken to a local medical centre for x-rays which revealed he had a fracture of his right scapula.
"Fortunately this doesn't require surgery but Edvald will return home to Norway for further investigation and treatment and we look forward to seeing him racing again sometime over the summer."
Team principal Sir Dave Brailsford added: "It's a real shame for Edvald and a setback for the team that he's been forced to abandon the race. It's never nice to lose a rider of Edvald's ability, but ultimately we're still confident that with the riders we've got left we can pull together and see the race through."
The 26-year-old's injury leaves the team with just seven riders in the race after Vasil Kiryienka missed the time cut on stage nine.
Boasson Hagen was the first Team Sky rider to secure a Tour de France stage win, taking stages six and 17 at the 2011 race.