The fly-half, 36 next week, is Ireland's most capped player with 128 appearances but has been in poor form this season.
After struggling against England in week two of the championship, and for Munster against Llanelli during the rest week, O'Gara's dreadful cross-kick deep in his own half was highlighted as Ireland lost to Scotland last weekend.
That performance appears to have been the final straw for coach Declan Kidney, who has named injury doubt Jonathan Sexton and the inexperience Paddy Jackson and Ian Madigan as his three fly-half options for Saturday's game at the Aviva Stadium.
Ulster's Jackson only won his first cap against Scotland and struggled with his goal-kicking while Madigan, of Leinster, has yet to represent his country.
Sexton, meanwhile, seems unlikely to feature after team manager Mick Kearney on Thursday rated his chances as "somewhat less than 50-50".
Like Sexton, locks Mike McCarthy and Donnacha Ryan and wing Craig Gilroy are included in the party despite struggling with injuries, but centre Darren Cave and U20 back Robbie Henshaw miss out due to concussion.
Hooker Dimitri Szarzewski has been ruled out of France's squad because of thigh and shoulder injuries.
The Racing Metro player, who picked up the injuries in his team's 23-3 win against Grenoble in the Top 14 on Saturday, has been replaced in the France squad by Perpignan's Guilhem Guirado.
"We made this change because Dimitri, because of his injuries, will not be able to train before Thursday. His participation in the game would then be 50-50," manager Philippe Saint-Andre said in a statement.
"That's why we called up Guilhem so that he can train as of tomorrow with the group."
France travel to Dublin on Saturday having lost their first three championship matches.