Struggling Villarreal lose Rossi for six months
The Italy international, who joins strike-partner Nilmar on the sidelines, suffered the injury in Wednesday's 3-0 defeat at Real Madrid, which left Juan Carlos Garrido's side in 18th with just seven points from nine matches.
They are also on the verge of elimination from the Champions League.
"Our worst fears have been confirmed," Villarreal said in a statement on their website.
The 24-year-old Rossi, who was born in the United States and had a stint at English Premier League side Manchester United, would be operated on later on Thursday at a clinic in nearby Valencia, they added.
Brazil striker Nilmar had knee surgery at the beginning of this month.