The Wall Street star and Rossi were celebrating her birthday at Giorgio Baldi restaurant in Santa Monica, California when they realised Rihanna was also dining there.
Sheen sent over a request to meet the R&B star but she declined because there were too many paparazzi photographers outside.
Now the actor has taken to Twitter.com to blast the 26 year old, stating: "Nice impression you left behind, Bday (birthday) or not. Sorry we're not Kool (sic) enough to warrant a blessing from the Princess. (or in this case the Village idiot)..."
He continues, "See ya (sic) on the way down, (we always do) and actually, it was a pleasure Not meeting you. clearly we have NotHING in common when it comes to respect for those who've gone before you. I'm guessing you needed those precious 84 seconds to situate that bad wig before you left the restaurant."
Rihanna has yet to respond to Sheen's comments.