Anything? Please. If that were the case, little kids would have a lot more broken noses and eye injuries than they do just from getting into pillow fights. I don't know about you, but when I was a kid, we didn't hold back swinging those pillows, and my nose is intact.
Secondly, we're talking about a pie here, not a baseball, hockey puck, or other heavy/hard object. Unless enclosed in a hard, heavy pan, a pie is just going to disintegrate on impact, and who would waste a good pan throwing it at someone? If your aim was to cause significant harm, there are far more effective options.
On a separate note, I think it's possible that your definition of "severe injury" may vary from many other people's; I just don't see a cut lip as being in that category, nor do I see how airborne baked goods could cause one. (Well, ok, maybe REALLY stale, dry bread...)