The France international, who won the last of his 15 caps in August last year, had to be replaced before half-time during the 3-0 home victory over Ajaccio in Ligue 1 last weekend because of a painful right knee.
"Further examinations showed he had torn his internal meniscus. He successfully underwent a surgery this afternoon," Lille said on their website (www.losc.fr).
The 25-year-old Martin has struggled to live up to expectations since he joined Lille last year from Sochaux for a club record fee of 10 million euros.
Lille are third in the table on 17 points from nine games, four behind leaders Monaco and champions Paris St Germain.