According to Brazil team doctor Rodrigo Lasmar, Alves will need at least six months to recover from the operation to repair a detached anterior cruciate ligament.
Dani Alves suffered the injury playing in Tuesday's French Cup final against Les Herbiers.
Dani Alves is confident that Paris Saint-Germain have what it takes to beat Real Madrid in their Champions League showdown in Neymar's absence.
It will be the ninth time Juventus, runners-up to Barcelona in 2015, have contested the final of Europe's elite club competition.
Neymar is rumoured to be wanting to leave Spain, especially following recent problems with the country's tax office. On the other hand, Dani Alves will be leaving Barcelona after a stint of eight years
Pep Guardiola will succeed in Manchester City, according to Barcelona defender Dani Alves
Dani Alves replaces injured Monaco right-back Fabinho for Brazil's opening 2018 World Cup qualifiers against Chile and Venezuela.
Barcelona will miss the services of Dani Alves for a month after he sustained an abductor injury.
The Catalan giants were defeated 1-5 on aggregate by Bilbao after a 1-1 second leg draw at the Camp Nou on Monday. Bilbao had thrashed Barcelona 4-0 in the first leg last week. This was the first trophy for the Basque club in 31 years.
'If you let the opportunity go by, you are not thinking about the team'
Dani Alves has replaced injured Real Madrid full-back Danilo in Brazil's Copa America squad.
Dani Alves's contract was due to expire on June 30 but he came to an agreement with Barcelona officials for the extension through to 2017, with the option of a third additional season.
Dani Alves's tenure with Barcelona expires later this month after a seven-year stay and the full-back has lately been linked to Paris-Saint Germain and Manchester United.
Dani Alves joined Barcelona from Sevilla in 2008 and has been a key component of the club's triumphs in recent seasons but has so far not agreed to extend his current deal to remain at Camp Nou.
Barcelona, the La Liga winners of the season, have Chilean goalkeeper Claudio Bravo, defenders Dani Alves and Gerard Pique, and Argentine striker Lionel Messi in the all-star squad.
Dani Alves has been heavily linked with a move to Paris Saint-Germain and Manchester United among a host of other top European clubs.
Barcelona coach Luis Enrique has also included Brazilian back Douglas for the first time since his signing for the Champions League game against APOEL Nicosia.