The fullback suffered an ankle injury in victory against Liverpool last week.
"Firstly I want to say to everyone thank you very much for the words of support, I read everything and see. I do not need surgery and now my goal is to recover as soon as possible and I hope to see you at the Euros," said Mykolenko.
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"For Evertonians, you have been amazing this season, particularly in derby. That's why I stood up after twist and played as much as I could.
"See you next season Toffees."