The Honduran was carried off on a stretcher during the 2-2 draw with Tottenham Hotspur last weekend, but it had been expected that he would return before the end of the season.
However, Martinez told reporters at a press conference: "We have had real negative news with Maynor Figueroa.
"He came off in the game really early and the scans have confirmed our worst fears. He is going to be out for the rest of the season and probably a longer period."
The 30-year-old will miss the club's last four league games in addition to the FA Cup final against Manchester City.