South Sudanese-Australian model Adut Akech says she has been deeply affected by the error in WHO Magazine and says Australia "has a lot of work to do".
In the magazine interview, she discussed people's attitudes to colour and her career in fashion.
WHO Magazine issued an apology, saying it had been given the wrong picture by the agency that set up the interview.
Ms Akech appeared in the magazine ahead of Melbourne Fashion Week. However the magazine printed an image of Flavia Lazarus, another model appearing at the show, instead.
In the interview, Ms Akech spoke about using her voice to start a conversation about how people viewed refugees. She fled South Sudan for Kenya where she resided in a refugee camp before seeking asylum in Australia in 2008.
Writing on Instagram after the error was made, the model said: "This is a big deal because of what I spoke about in my interview. By this happening, I felt it defeated the purpose of what I stand for and spoke about."
She added that she wanted the incident to be a "wake-up call to people within the industry".
WHO Magazine said it had spoken with Ms Akech directly to apologise and "to explain how the error occurred".
Melbourne Fashion Week published an apology on its Instagram page: "We are extremely disappointed that a photo of one of our campaign models, Flavia Lazarus, was mistakenly printed instead of a photo of Adut.
"Both Adut and Flavia have expressed their disappointment and we support them. This error is unacceptable, and both Who Magazine and our public relations agency, OPR, have apologised."
OPR said in a statement quoted by ABC: "The error was administrative and unintentional and we sincerely apologise for this mistake and any upset it has caused to the models involved, and our client the City of Melbourne."