Stoica, born in Romania and known as Alessandro to his team-mates, was declared unfit during training on Tuesday and the 25-man party has been trimmed to 24.
Stoica, who can play at centre, wing and full-back, had been nursing a strain to his right thigh and medics with the team decided he would not be able to play in Sunday's match and the player has returned to his French club Castres.
On Monday, reserve scrum-half Juan Manuel Queirolo was also forced out with an injury, with Matteo Mazzantini of Rovigo called up as a replacement understudy for Italy skipper Alessandro Troncon.
Coach John Kirwan is expected to announce his team for the France match on Wednesday.
Italy got off to a winning start, beating Wales 30-22, but have lost their subsequent matches to Ireland and England.