Initially scheduled to take place in the summer, this year's AFCON was scheduled for December 21st - January 18th, depriving leading European clubs of key players participating in it at a crucial stage of the domestic season.
"Everybody wants to play in AFCON. It's one of the best competitions in the world," Chukwueze told On Sports TV.
"You have to respect the AFCON the same way you respect the European Championship or World Cup."
The Fulham winger will miss six games for his club if Nigeria reach the round of 16.
"We understand they scheduled it at the wrong time of the year, but when it's important, if you get recalled you have to go," he said.
"You don't have any choice, your club can't stop you and no one should say anything bad about the AFCON. Yes, they put it at the wrong time, but saying it's not a good competition or a great competition is unacceptable."
Chukwueze helped Nigeria secure an opening 2-1 win over Tanzania in Group C ahead of their second game against Tunisia on Saturday.