The 31-year-old has been ruled out of matches for club and country, joining Lacina Traore on the Toffees treatment table, though a "refreshed" Romelu Lukaku returns to the squad.
It means Jagielka will miss the Wembley friendly on March 5, with Roy Hodgson set to announce his squad for the fixture on Thursday afternoon.
Martinez told reporters: "Phil has felt his hamstring over the last couple of days and will be missing at the weekend and for England.”
The Toffees also suffered a blow by losing Lacina Traore to injury in the pre-match warm up at Chelsea last weekend and Martinez is unsure when the Ivorian will return.
"Today we will discover the best possible route to go down in terms of the treatment for Lacina," he added. "We're working with Monaco."
Everton has lost three of its last four top flight games, including two narrow 1-0 defeats to Tottenham and Chelsea, but Martinez believes his team can take heart from their performances, if not points.
"We haven't been able to get the results our performances have deserved recently and that's something we need to work on," he said. "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 and know we can count on our fans. West Ham are in a good run of form and we're going to see a side full of confidence. Sam Allardyce deserves a lot of credit."
Martinez also paid tribute to the returning Romelu Lukaku, who has missed the entirety of February with an ankle injury, adding: "I'm really excited about seeing Romelu again. It's been the most demanding season of his career and the break has refreshed him."