Scotland head coach Gregor Townsend confirmed the Glasgow Warriors back will undergo surgery today (Thursday) after being forced off late in Saturday's 31-20 Calcutta Cup win at Murrayfield.
The injury will rule Dobie out for the rest of the Six Nations and a significant portion of Glasgow's season.
"Jamie Dobie is getting surgery today (Thursday) on his shoulder so he'll be out for the tournament," Townsend said.
"We obviously don't know how that surgery is going to go. It's a pretty routine operation to stabilise the shoulder."
Asked about his recovery timeframe, Townsend added: "It'll be months," before saying: "Whether that's more than four months, more than three months, we'll wait and see but he's definitely going to be ruled out for the rest of the tournament."
There was also an update on Jack Dempsey, who is likely to miss the rest of the Six Nations with a bicep injury.
"Jack is still getting different opinions on his injury," Townsend said.
"He might not be out for a long period. But if it is surgery, again, that would be him out for a couple of months minimum."
Townsend believes Dempsey could still contribute at club level, adding: "I think he's very unlikely to come back for us, but he could play a big part in the season with Glasgow."