Alves, who plays for French champions Paris St Germain, limped off near the end of Tuesday's French Cup Final win over third-tier Les Herbiers.
The Brazilian team doctor, Rodrigo Lasmar, flew to Paris to examine the player and decided surgery was necessary after diagnosing an injury to his right anterior cruciate ligament.
"It is clear that the Daniel Alves’s call up for the period of preparation, friendlies and consequently the World Cup, is impossible," the Brazilian Football Confederation CBF said.
Brazil will play warm-up matches against Croatia on June 3 and Austria seven days later, before kicking off their World Cup campaign on June 17 against Switzerland.
The five-times world champions will then play Costa Rica and Serbia in Group E.
Alves, 35, is one of the squad's most experienced players with 107 caps.
His absence in Russia will be a blow to Brazil coach Tite, who values not just his technical ability but also his effect on the dressing room, where he is one of the most popular players.
The right back, who is a fine crosser of the ball, is expected to be out for up to six months and Brazil's players past and present expressed their support for Alves.
"I am so sad to hear this. Footballers hate missing games but I know first-hand that missing World Cup games is the worst feeling," Pele, who was forced out of the 1962 and 1966 World Cup tournaments because of injury, said on twitter.
Manchester City's Danilo and Fagner of Corinthians are among the players most likely to replace Alves when Tite announces his 23-man squad for the finals on Monday.
(Reporting by Andrew Downie; Editing by Toby Davis and Ken Ferris)
