The highly-rated centre back has been plagued by injury problems all season, and picked up his latest knock in last weekend's league clash with Malaga.
The news comes as a bitter blow to both the player and his manager, Miguel Angel Lotina, who has been frustrated by Sergio's unfortunate run of injuries.
"Of course, it's something that worries all of us," said the Celta boss of Sergio's most recent setback.
"He is one of the best centre backs in Spain and, unfortunately, we are not able to call on him."
With Sergio now out, and Sebastian Mendez having returned to Argentina for treatment on a knee ligament injury that has ruled him out for the rest of the season, Lotina has been left with a defensive headache.
The former Osasuna boss only has two front-line central defenders available, Fernando Caceres and Eduardo Berizzo, and may now be forced to use Spanish international Juanfran in a more central role for this weekend's league clash with Valencia.
