The former Spain striker, who has been out of favour at his club and has not played since early October, went under the knife at a hospital in the Spanish port city on Monday afternoon, Valencia said on their website (www.valenciacf.com).
They did not say whether the surgery was successful or how long the 30-year-old might be sidelined but local media said he would be out for a month.
Reports in Spain have suggested coach Nuno dropped Negredo because he was unhappy with comments the player made about tactics in a newspaper interview but the Portuguese has said the decision was "purely sporting".
Negredo joined Valencia from English Premier League side Manchester City in the close season for a fee of around 30 million euros ($32 million) but has yet to reproduce the form that earned him 21 Spain caps, with his most recent appearance for his country coming in November 2013.
($1 = 0.9358 euros)
(Writing by Iain Rogers, editing by Ian Chadband)
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