The Liverpool striker, who underwent a knee operation on May 22, has trained with the rest of his team-mates since Thursday but Tabarez has chosen not to risk the 27-year-old.
Tabarez said: "The doctor told us that Suarez was not going to be ruled out of playing at the World Cup and that is why he was not left off of the list.
"We are increasing his work rhythm and we hope that from now on he has no further issues."
Uruguay finished fourth at the World Cup in South Africa four years ago and at last year's Confederations Cup.
They are considered favourites for the encounter at the Estadio Castelao.
"We are professional and we are focusing on the difficult game we face tomorrow," he said. "Costa Rica have qualified for this World Cup, they have a lot of virtues and we will try to limit them.
"They are a fast side and very technical.
"But we are completely ready to compete and we want to play our games in the best possible way."
Unlike all of their group rivals, Costa Rica have never won the World Cup.
Costa Rica coach Jorge Luis Pinto expects a stern test against La Celeste.
"Uruguay are always a difficult team to play against," he said. "Then you have Italy and England, eternal European powers.
"The fact that we are facing such strong teams makes us hungrier to have a great tournament."
Dave Myrie has replaced Heiner Mora after the defender was ruled out of the tournament earlier this week with a stress fracture in his right heel.
Costa Rica captain Bryan Ruiz said: "These situations united the group much more and give us more reasons to go out and fight."
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- Edinson Cavani