La Liga - Rossi out for six months
The 24-year-old, who has scored three goals in nine Liga matches this season and in two Europe, suffered a cruciate ligament injury an hour into the 3-0 league defeat to Real Madrid on Wednesday night.
"Our worst fears have been confirmed," Villarreal said on their website.
The blow rules him out of the rest of the Champions League group stages, and much of the knockout phase if they qualify from a group containing Manchester City, Napoli and Bayern Munich.
Villarreal have struggled this season and lie 18th in La Liga, with seven points, and bottom of Champions League Group A having lost all three matches so far.
Rossi, who was born in the United States and had a stint at Manchester United, would be operated on later on Thursday at a clinic in nearby Valencia, they added.