The newspaper said Murray, the No. 2 pick in the 2012 NHL Draft, was hurt trying to break his fall and may have dislocated the shoulder.
"It's not good news," Blue Jackets general manager Scott Howson told the Dispatch. "Right now his arm is in a sling, held tight to his body, and he's in a lot of pain. He'll have an MRI [exam] early this week, and then we'll know more.
"You'll have to see how much damage he's done to the labrum. Does he have any broken bones from the thrust of the fall? Once it's come out, it tends to come out easier in the future. Our doctors will take a look at the tests and we'll decide the next step."
It is unknown how long Murray will be sidelined. After the 5-0 loss to Victoria on Friday, the defenseman had two goals and 15 assists in 23 games.
He was captain of Team WHL for one game during the recently completed Subway Super Series against Russia. He also was a contender to play for Canada in next month's World Junior Championship in Ufa, Russia.
NHL.com ranks Murray as the Blue Jackets' No. 1 prospect.