Manager Roberto Martinez confirmed on Wednesday that the 29-year-old, a £6 million close-season signing from Wigan Athletic, will go under the knife after suffering the setback as a second-half substitute in last month's victory over Hull City.
The Ivorian requires a procedure to remove some loose cartilage from his knee and, though the extent of his absence is not yet known, Martinez expects to be without him for a significant spell.
"We had to send him for a surgery and we need to see how long exactly he'll be out but it'll be a while," the Spaniard told the Liverpool Echo.
"I would say the worst fears were confirmed and he had some loose cartilage in his knee. We'll know in the next 48 hours.
"He needs it repaired and the loose cartilage taken out. It takes a long time to recover.
"We'll need to see how he gets through surgery but it's a really difficult injury in terms of time.
"He'll be fine long term but it's disappointing because I felt he showed against Hull he was ready to be himself and enjoy his football.
"We'll make sure he gets back fit and strong as ever."
Kone joins midfielder Darron Gibson on Everton's long-term injured list, with the Irishman having undergone an operation on his cruciate knee ligaments last week.
Martinez, who drew comparisons between the two injuries, remains hopeful that both players could return this season.
"It's similar to Darron, although Darron had already surprised everyone with how he's recovering because he's been around and put weight on his knee," he said. "He's very positive.
"If we could get them both back before the season ends it would be the best two signings."
