The 36-year-old was withdrawn at half time during the Toffees' 2-0 win over Manchester United, and will have a scan on Monday to determine the length of his absence.
Martinez told the club's official website: "Sylvain will have a scan tomorrow. He felt his hamstring. I just hope we pulled him out of the game just in time.
"If it's damaged, it will be difficult for him to play again this season. But, if not, maybe within a week or 10 days he will be fine."
Everton are fifth in the Premier League, one point behind Arsenal in fourth place.