The 31-year-old missed the Toffees' 2-1 win over Southampton on Sunday due to the injury, with summer signing Antolin Alcaraz replacing him alongside Sylvain Distin in defence.
Jagielka had been ever-present in the Premier League for Everton so far this season, but Martinez says that the defender is now set for a spell on the sidelines.
"It was at the end of the game against Sunderland," he said.
"With this soft tissue injury it could be up to four weeks, but knowing Jags he will be back earlier.
"It is just the accumulation of games and the demands of this month - November into December is high-risk in terms of injuries to the players.
"When you have the number of games we play, it is understandable."
Martinez also spoke of Romelu Lukaku netting for the first time in six games, saying that there are other aspects of the striker's game that have pleased him during his dry spell.
"From the outside, yes, you are going to judge a striker by his goalscoring ability and the numbers," he said.
"But for me, if he scores goals, great - but it is a bonus. I judge him in terms of all the aspects. I thought he was magnificent against Swansea (a recent 2-1 win) without scoring.
"I couldn't be happier with his finish today, but I think that is an add-on."
Asked if Lukaku had suffered a dip in morale due to his run without scoring, Martinez added: "No - we have been working on other aspects of his game.
"We have never been in a position where we were getting a little bit worried and thought that was his only role as a striker.
"You want strikers to score goals, but in the same way, he attracts two or three opposition players at the moment, so it is understandable that other players get that stage - players like Seamus Coleman, who gets into that position really well and takes advantage of it.
"It is a team effort and Romelu has not been down at all - it has been the opposite."
Martinez also defended Joel Robles, despite the goalkeeper failing to deal with Gaston Ramirez's long-range strike for Southampton's equaliser.
"Joel is blaming himself, but I don't think that is the case," he said.
"It is one of those goals where when you watch the replay, you feel the goalkeeper should have had it.
"But I thought when I watched it live; you should probably blame the people who design these footballs.
"If you hit them well, they swerve everywhere and it becomes a gamble for the keeper - it can hit the arms, it could have gone anywhere.
"When you watch it live, I don't think Joel is to blame. I think Gaston Ramirez hit the ball really well.
"I thought Joel had a really good game - he was in control of his box, and showed great understanding with two centre-halves he has never played with before."