The 22-year-old forward has struggled with injuries this season and has not played for the first team since March 1.
He has already been ruled out of Scotland's friendly international against Nigeria at Craven Cottage on May 28 but will be ready for his club's European games which could start as early as July 16.
Hoops boss Neil Lennon told the Evening Times: "Jamesie will not be going away with Scotland at the end of this month.
"He has had surgery on his groin and needs a bit of time to recover.
"I don't know if Nir Biton, who has been out for a few months, will be going away with Israel. But we are hoping he can."