The 31-year-old, who has 24 caps, will also miss Saturday's Premier League game against West Ham United and is a doubt for Everton's FA Cup quarter-final at Arsenal on March 8.
Martinez told reporters at his pre-match briefing: "Phil has felt his hamstring over the last couple of days and will be missing at the weekend and for England. I don't think its long-term."
The Merseysiders will also be without Ivorian striker Lacina Traore after the loanee injured his hamstring in the warm-up for the Premier League clash against Chelsea last weekend and faces "weeks" on the sidelines, according to Martinez.
Everton, seventh in the table and chasing a Europa League spot, are level on points with sixth-placed Manchester United and five points behind fifth-placed Tottenham Hotspur, and losing Jagielka will be a blow to their chances.
Martinez continued: "The only focus we have is to get as many points as we can between now and the end of the season and get where we deserve to be.
"We know we'll have to be at our best against West Ham, but we're happy to be at Goodison Park and know we can count on our fans."
England manager Roy Hodgson is announcing his squad for the Denmark match later on Thursday and Martinez believes there should be a recall to international duty for midfielder Gareth Barry, who won the last of his 53 England caps in May 2012.
"I think Gareth Barry is ready to help England," the Spaniard said. "The experience he brings is quite unique. It would be a great honour if he got a recall."
(Reporting by Mike Collett; Editing by John O'Brien)
