"As you would expect, I'm very upset," said Nihat, who sustained the injury shortly before halftime in his side's 1-0 victory at home to Sevilla on Saturday.
"I can't do anything about it now and I have to look ahead to the future. I hope the team does well in the rest of the season and I'll be there cheering them on.
"I'm going to have to be very patient because there are a lot of months of hard work ahead of me."
It is not the first time Nihat has had to be operated on to deal with problems in his left knee.
He was originally due to sign for Sociedad in December 2001, but the deal was put on hold after he had surgery after suffering cartilage damage.
Nihat eventually joined the Basque side a little over a month later for a club record fee of $4.80 million.
He played a key role when Sociedad finished runners-up to Real Madrid in the 2003 title race, scoring 23 goals as he formed a prolific strike partnership with Serbia & Montenegro striker Darko Kovacevic.
He scored 14 goals last season and is the club's leading scorer this term with 13.
