The 31-year-old Jagielka picked up the injury in training last week and was absent from England's victory over Denmark on Wednesday.
"It's unlikely Phil Jagielka will be involved on Saturday," Martinez said at a news conference.
"With Phil we are going to give him as long as we can but if the game was tomorrow he wouldn't be able to play.
"Apart from Phil and the long-term absentees, everyone else is fully fit and available."
Martinez, who won the FA Cup last season while in charge of Wigan Athletic, remains cautious though and has called on his side to rise to the occasion.
"It is a glamorous tie and we are looking forward to it," added the Spaniard.
"There is never a good or bad time to face a top team. We admire them immensely.
"They had a disappointing result last weekend but that doesn't change anything.
"If you want to be winning a competition like the FA Cup, you have to find a way to be effective against a team like Arsenal."
Martinez also confirmed that on-loan Monaco striker Lacina Traore is to stay with the club as he tries to recover from a hamstring injury.
"We are working with Monaco but we are going to take the leading role," he added.
"We have seen the specialist and everything has been organised for us with a specific treatment for the next six weeks."
- Sports & Recreation