The Ivory Coast forward, yet to open his account for the Toffees, missed his side's 2-0 win over Aston Villa with a knee problem, though the club are hoping he will return soon
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And Martinez has confirmed that the forward's omission was due to a knock he suffered in his last appearance, although the Spaniard does not expect Kone to be out for long.
"It [the knock] was during the last game against Hull City," Martinez told the club's official website.
"He received the ball and then got a strong challenge on his knee.
"We're hoping that it's not going to be too much of a serious problem, but he's going to miss the best part of four days."
Kone, who worked under Martinez at Wigan, moved to Goodison Park from the Latics in the summer, but has yet to start a Premier League game for his new club or find the back of the net.