UNDER the prop shaft? So it protects the road from heat? There is a heat shield OVER the prop shaft that keeps heat from migrating from the tunnel into the passenger compartment. Under the prop shaft sounds more like an under tray component, which is for aerodynamics, not heat protection.
if so, safe to drive, but you should get it fixed at some point. Disclaimer: I'm going on memory, I'm too lazy to raise my car to confirm what I think I remember.