Anichebe told the BBC in an interview he has put his international career on hold "so he can manage his body accordingly."
It comes after litany of injures for the striker, including a groin problem in his last international appearance against Madagascar in an African Nations Cup qualifier two years ago.
"The best thing for me at the moment is to focus on club football," the 25-year-old said.
"Without club football there is no international football and everyone at Everton was with me every step of the way during my injuries and rehabilitation and so I owe it to the club to manage myself correctly.
"I didn't feel that the Nigerian federation was there for me then in the same manner, which was especially disappointing given that I got the injury representing my country," he added.
"But I don't blame anyone for this nor do I have any issues with anybody from the NFF or Stephen Keshi our coach.
"The time is just not right for me to resume my international career as of yet but I would certainly love to represent my country in the none-too-distant future."
Nigeria qualified for the eight-team tournament from June 15-30 after winning the African Nations Cup in South Africa in February.