The back-row forward was forced to return home early from the British & Irish Lions' trip to New Zealand with a hamstring problem - four years after a knee injury ruled him out of the previous tour.
Now the 25-year-old will require further rest after suffering a strain in training this week.
Edinburgh rehab physiotherapist Stephen Mutch said: "Simon was running freely on Monday when he over-reached in a contact situation which was disappointing given the quality of his pre-season.
"He's currently on a recovery programme and will be subject to further assessment next week."
Meanwhile, Chris Paterson has been named Edinburgh captain this season as the club welcomed Apolosi Satala to the squad.
Scotland international Paterson will have Scott Murray as his vice-captain this year and the 27-year-old is relishing the prospect of the new campaign.
Paterson said: "I'm excited, the same as everyone else at Edinburgh.
"We're just desperate to play games and desperate to put into action the fitness we've been put through."
Fiji World Cup sevens winner Satala is set for his first appearance for Edinburgh against Leeds Tykes this weekend.
The 27-year-old back-row forward, who is a serving solider with The Royal Scots, has been released to the Gunners temporarily and will be available unless required by the Army for rugby or operational duties.