Liverpool’s Premier League Player of the Year injured his knee in training on Wednesday giving his side a major World Cup scare, the report said.
The Uruguayan team and federation made no immediate comment.
Suarez, top scorer in the English league this season with 31 goals, “felt pain in training” and an MRI scan detected a meniscus problem, a leading television reporter Martin Charquero posted on Twitter.
Charquero said that Suarez’s brother Paolo Suarez had confirmed the injury to him.
Despite the proximity of the World Cup in Brazil, the reports said there is still hope the 27-year-old could play a role in the tournament.
Uruguay’s hopes will depend on the severity of the damage found by surgery.
Experts said it normally takes four to six weeks to recover from the operation.
Suarez only arrived in the Uruguayan capital on Tuesday, but insisted he was anxious to start training with his teammates.
He enjoyed a stunning comeback in the 2013/14 Premier League campaign after his reputation plummeted for racially abusing Manchester United’s Patrice Evra and then biting Chelsea’s Branislav Ivanovic.
His brilliant sharp-shooting inspired Liverpool into second behind champions Manchester City.
Uruguay are drawn in Group D in the first round of the World Cup.
They face Costa Rica on June 14, followed by England on June 19, and Italy five days later.
Uruguay have two World Cup warm-ups scheduled, against the Republic of Ireland on May 30 and Slovenia on June 4, both games to be held in Montevideo.