The Liga club confirmed in a statement that the Spain striker was rushed to hospital and went under the knife.
No comment was made on how long Negredo was expected to be out for, but reports suggest he will be sidelined for at least a month.
It has been a frustrating season for the former Manchester City man, who has not featured for Los Che since a 3-1 defeat against Athletic Bilbao on October 3.
Negredo criticised head coach Nuno Espirito Santo in an interview following a slow start to the season, and the fans backed the player, whistling Nuno during the 3-0 victory over Levante.
Nuno talked down a rift between himself and Negredo, insisting earlier this month that the 30-year-old's absence from the first team was owing to performance-related issues.