Some of the biggest names in England's top flight, including Liverpool's Mohamed Salah and Sadio Mane, will be playing in the 24-team event that starts on 9 January, missing crucial games for their clubs.
Wright said the tournament was being treated differently from Euro 2020, which took place earlier this year, highlighting the issue of player release.
In a video posted on his official Instagram account on Wednesday, the former Arsenal forward said: "Is there ever a tournament more disrespected than the Africa Cup of Nations?
"There's no greater honour -- none -- as a sportsperson than representing your country. The coverage is completely tinged with racism, completely tinged.
"We played our Euros across 10 countries in the middle of a pandemic and there's no issue, no issue at all. But Cameroon, a single country hosting a tournament, is a problem?
"You're getting players being asked if they will be honouring the call-ups for their national teams, if they will be 'honouring'. Imagine if that was an English player representing the Three Lions?"
Wright said many of the best players in the European leagues were African.
"If we love them at club level, why can't we love them at international level like their counterparts from across the globe?" he asked. "Why can't we?
"Why is this tournament constantly getting so much flak?"
Wright received the backing of former Barcelona striker Samuel Eto'o, the president of the Cameroonian Football Federation.
Eto'o tweeted: "Respect @IanWright0. There's no greater honour for a sportsperson than representing your country. The Africa Cup of Nations is a celebration of African pride, and next week's AFCON will once more prove the undeniable greatness of African players."
Crystal Palace boss Patrick Vieira had earlier issued a similar call for respect for the tournament, a message reiterated by Ajax's Ivory Coast striker Sebastien Haller.