Liverpool's Premier League Player of the Year injured his knee in training on Wednesday giving his side a major World Cup scare.
Suarez, top scorer in the English league this season with 31 goals, ‘felt pain in training’ and an MRI scan detected a meniscus problem.
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.
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.
Host stadium’s second test delayed
A second test event for the stadium hosting the opening match of the World Cup on June 12 has been put back three days to June 1, according to Fifa.
Organisers decided a new dress rehearsal was needed at Sao Paulo's Corinthians Arena after its first major test event, a Brazilian league match Sunday, revealed a host of problems.
"It is vital for us that all facilities will be tested under full match conditions including the temporary seats and associated facilities," said Fifa Secretary General Jerome Valcke.
Fifa said in a statement the new event needed to draw more than 50,000 fans and test two extra seating areas that were not yet open at Sunday's match because they had not received safety clearance from fire fighters.
About 36,000 fans attended Sunday's match, well below the 68,000 expected for World Cup games.
Organisers are still scrambling to get the stadium finished in time for the World Cup opening ceremony and kick-off match between Brazil and Croatia.
The remaining 11 World Cup stadiums are all due to be handed over by the end of the week. Work is still not finished at the stadiums in Curitiba, Cuiaba and Porto Alegre.
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