The Ivory Coast international picked up the injury in the win over Hull two weeks ago, but Roberto Martinez has revealed it is worse than originally thought and he now needs surgery and may struggle to play again this season.
The £6million summer signing from Wigan has had no timescale placed on his recovery but Martinez believes he, like Darron Gibson, is in a race against time to feature again during the current campaign.
"We had disappointing news (in that Kone) will need a bit of a period away," Martinez told evertontv.
"We need to give him a lot of support because he was enjoying his role when he came on against Hull and then he got a nasty incident that is going to keep him away for a long time.
"He had a loosened body, a bit of cartilage in his knee, so we need to repair that which will take time.
"We're going to work on other aspects of his body to get him fully fit and strong so that when he comes back, he is ready to enjoy his football.
"It's going to be a long spell out and that's disappointing.
"We've got Darron Gibson reacting really well a couple of weeks after (knee) surgery so now he and Arouna are going to work extremely hard to get back before the season ends."
The news on Kone's fitness leaves Martinez short of options up front, with Romelu Lukaku and Nikica Jelavic the only recognised strikers in the squad, although Gerard Deulofeu and Steven Naismith have been used in attacking roles.
Everton last week