Stuart Hogg hopes to return from a “in the next couple of weeks”, with Scotland’s Six Nations campaign beginning on 3 February.
The full-back, 25, sustained the damage ahead of Scotland’s autumn Test victory over Australia in late November.
Hogg, a two-time British and Irish Lion, has 55 Scotland caps.
“Hopefully I’ll be back on the pitch in the next couple of weeks and ready to rock and roll again,” Hogg told BBC Radio 5 live’s
The Hawick native, who missed the Lions Test series after being injured early in the tour, pulled up injured in the warm-up before Scotland hammered the Wallabies by a at Murrayfield.
Gregor Townsend’s side open their Six Nations account against Wales in Cardiff, before hosting France eight days later.
“We’re getting there now,” Hogg said of the injury.
“I actually did it midweek. The place we train for Scotland, you’ve got about five metres between the try-line and a brick wall, and I’d been running full pelt to score a try and then had to stop suddenly, and I think I pulled it.
“In the warm-up, I kicked the ball and I felt as if somebody had stabbed me in my hip. It was a bit frustrating because I was just coming back from a long-term shoulder injury, I was feeling good, starting to get a little bit of form back and had to start back at square one.
“I’ve never really picked up any injuries – to end up getting a fractured eye socket, then have to get your shoulder operated on, it has been a bit frustrating.”