The striker has formed a good partnership with Franco Di Santo since joining the club in the summer, the pair scoring six goals between them, but could miss a month of domestic action on duty with Ivory Coast. Martinez told Latics Player:
"It's always great to be involved with the national team and playing in these big tournaments so that's always a positive, but not at the expense of missing games with your club. That's a real disappointment.
"It's a long period of time for us not to have Arouna. You can't do much about it but we're going to really look forward to seeing him at his best while he's here with us."
Kone, 28, was part of the Ivory Coast squad caught up in a riot that caused the abandonment of their qualifying game in Senegal at the weekend, leading to Senegal's expulsion from the competition. Martinez added:
"You're always concerned about what could happen when players are away. I thought the Senegal authorities handled the situation well, they protected the players and took them away from the ground. Arouna is fine, as are all his team-mates."