Fischetti suffered "three costal cartilage fractures on the left side of the thorax," during Friday's bruising defeat to New Zealand, FIR said.
The 35-time capped loosehead prop was forced off the pitch after 18 minutes as Italy fell 96-17 in a defeat which left its mark, with two other players doubtful for the France showdown.
Lock Dino Lamb (25) picked up a left leg injury and will have further tests in the coming days, while hooker Giacomo Nicotera (27) is subject to a concussion protocol.
Italy have already lost experienced hooker Luca Bigi (32) to an adductor muscle injury.
The Azzurri are thrid in Pool A with ten points and must beat group leaders France next Friday in Lyon to reach the quarter-finals for the first time.
