"It will be weeks rather than months," Martinez told the club's website (www.evertonfc.com). "It is a soft tissue injury in the hamstring very similar to a previous injury he had.
"It is going to take a long period of time which at this stage of the season will be a big miss.
"It's a really disappointing outcome. He was ready and had been working really hard since he arrived at the club."
But Everton have been boosted by the impending return of top scorer Romelu Lukaku, who has been out with an ankle problem.
"Romelu has been working really well and he is looking fresh and ready," said Martinez, whose side are seventh in the Premier League on 45 points from 26 matches.
"We are all very excited to see him back enjoying his football with really top energy levels." Lukaku is on loan at Everton from Chelsea.
(Reporting by Michael Hann; editing by Robert Woodward)
