The club says the players have been scheduled to undergo the procedure Friday to solve recurring throat problems.
Neymar will be operated on in Rio de Janeiro under Barcelona's medical supervision, while Alba will be treated in Barcelona.
The club says surgery was delayed until the Confederations Cup ended. Brazil trounced Spain 3-0 Sunday in the final.
Neymar completed his move to Barcelona on June 3 on a five-year deal that pairs him with Lionel Messi in a formidable attacking partnership.
The club says "recovery time in both cases is about 10 days."
Alba is due to arrive at Madrid airport with the rest of Spain's squad later Monday.