The 35-year-old Paris Saint-Germain defender injured the cruciate ligament in his right knee during his side's routine French Cup victory over Les Herbiers on Tuesday.
Daily Mail citing Fox Sports Brazil disclosed that his national team coach Tite has started shopping for possible replacements before he names his 23-man squad for the finals in Russia on Monday.
"Following this line of work together, the patient underwent a detailed examination and confirmed the initial diagnosis of an anterior cruciate ligament injury, which required surgical treatment".
Alves is the third most capped player for Brazil with 107 appearances and seven goals since he made his debut with the team on October 10, 2006.
Tite has previously played Manchester City's Danilo, Corinthians' Fagner, and Bayern Munich's Rafinha. The raiding right-back will be missed, since he still has the pace, engine and technique to be a vital outlet in attacking areas, even in the winter of his career.
"Under these conditions, the player, PSG's medical staff and Brazil's medical staff have decided that surgery is the best option".
In the end, it's a tough blow for this team and one manager Tite will surely lose a bit of sleep over as he tries to solve his starting XI.
He also played in the World Cup in 2014, when hosts Brazil infamously lost 7-1 in the semifinals to Germany.