The 26-year-old was originally pencilled in as part of the Scotland A side to play against their French counterparts in Agen on Saturday.
But Bristol Shoguns back-row forward Ross Beattie has been ruled out of the Paris game with a recurrence of the Achilles injury which affected him last autumn.
He said: "I'm extremely disappointed. There was a chance I'd be fit for this weekend's 6 Nations game. But I need to rest the Achilles for a few days and the team travel to France on Thursday."
Petrie feared his RBS 6 Nations hopes were over last month when he suffered a thumb injury playing against Edinburgh Gunners in January.
But tests revealed the injury would not require surgery and the Dundee-born player would be available for the tournament.
Petrie will be replaced at number eight in the Scotland A team by Eric Peters of Connacht.
The other change sees Glasgow's Jason White win a place among the forwards at the expense of Edinburgh's Nathan Hines, as Ian McGeechan seeks to put Sunday's 36-6 defeat to Ireland behind him.
Scotland squad to play France at the Stade de France:
Backs: M Blair (Edinburgh), A Craig (Orrell), B Laney (Edinburgh), K Logan (Wasps), G Metcalfe (Glasgow), C Paterson (Edinburgh), B Redpath (Sale, capt), G Ross (Leeds), G Townsend (Borders), K Utterson (Borders).
Forwards: J Petrie (Glasgow), G Bulloch (Glasgow), B Douglas (Borders), S Grimes (Newcastle), G Kerr (Leeds), M Leslie (Edinburgh), A Mower (Newcastle), S Murray (Edinburgh), S Scott (Borders), T Smith (Northampton), S Taylor (Edinburgh), J White (Glasgow).