Alves had to come off in the second half of Saturday's 3-2 La Liga win at Almeria and Valencia said on their website on Sunday (www.valenciacf.com) tests had revealed damage to the external cruciate ligament and meniscus in his right knee.
With an operation required the club did not say how long the keeper might be sidelined, but Spanish media reported he would be out for around six months.
If that is the case Alves will not return to action until November and therefore miss qualifying matches for Europe's elite club competition.
"We are happy and pleased with the victory but sad for Diego Alves," executive president Amadeo Salvo said after Valencia secured fourth place behind champions Barcelona, second-placed Real Madrid, and Atletico Madrid who finished third.
Valencia are now close to making a lucrative return to the group stage of the Champions League following their takeover late last year by Singapore billionaire Peter Lim.
Hopes are high among fans that Lim's investment will help the club sort out their finances and make them genuine contenders in Spain and Europe again.
Champions League finalists in 2000 and 2001, Valencia missed out on European competition after finishing eighth last term with a mere 49 points.
They ended their latest La Liga campaign on 77 points, the same number they amassed when they last won the Spanish league title in 2004, a point behind Atletico.
"We have completed our objective for the season," Amadeo said. "Now we have to look to the future. We have a project that will continue to grow and develop."
With some wise spending over the summer Valencia, under Portuguese coach Nuno, could make a strong challenge next term in both domestic and European competition.
(Reporting by Iain Rogers, editing by Amlan Chakraborty and Douglas Beattie)
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