The 27-year-old won the PFA and Football Writers' Player of the Year awards after a superb season with Liverpool, but it is understood he twisted his knee in training with his country on Wednesday.
The Uruguayan Football Association is optimistic that Suarez will be fit for the World Cup, with his team kicking off their Group D campaign against Costa Rica on June 14 before facing England five days later and then Italy.
Uruguayan FA official Roberto Pastoriza told Ovacion that surgery was looking very likely.
"According to the report I received a while ago, they are optimistic that he can play the World Cup," said Pastoriza.
"Suarez felt discomfort in his knee and thus he had to undergo tests. Everything happened very fast, some hours ago (on Wednesday night).
"The national team medical staff is dealing with this and press secretary Matias Faral will communicate the official report.
"The intention was that everything was kept confidential and that the report was announced today through the Uruguayan FA social network accounts.
"Everything was very surprising, Suarez trained with discomfort and it was decided to have an MRI scan.
"The information until a while ago was that they were deciding what will be done, but there are very high chances there will be a surgical intervention.
"I can't say anything else, the Uruguayan FA will officially announce it on Thursday morning."
The former Ajax forward, who scored 31 goals in the Premier League as Liverpool fell just short of a first league title in 24 years, returned to Uruguay on Tuesday to train with the national team, who he helped reach the World Cup semi-finals in 2010.
Suarez has won 77 caps for his country and forms a key part of an impressive array of attacking talent in the squad, alongside Paris St-Germain striker Edinson Cavani, veteran Diego Forlan, Palermo's Abel Hernandez and Espanyol's Christian Stuani.
It is understood Liverpool's medical team are trying to ascertain the full extent of Suarez's injury.
Suarez will almost certainly miss Uruguay's pre-World Cup warm-up games against Northern Ireland on May 31 and Slovenia on June 5.