Argentina midfielder Fernandez wore the captain’s armband during Chelsea’s opening Premier League defeat to Manchester City on Sunday.
Chelsea club captain Reece James was suspended for the Stamford Bridge clash but many fans questioned Enzo Maresca’s decision to let Fernandez lead the side out.
Fernandez was forced to apologise after uploading a video to social media which the French Football Federation said included a ‘racist and discriminatory’ chant.
The 23-year-old, who cost Chelsea more than £100m, said he was ‘truly sorry’ for the video, which was taken as Argentina celebrated winning the Copa America.
The apology came after Chelsea team-mate Wesley Fofana described the footage as ‘uninhibited racism’.
Ex-England striker Wright believes there is ‘no way’ Fernandez deserves to be captain following the racism row and says Chelsea need to ‘fix themselves’.
Speaking on the Wright’s House podcast, he said: ‘Chelsea man, oh my god. Fix up yourselves. What are they doing?
‘There’s no way that man deserves the captaincy. It’s embarrassing.’
Wright also said that Fernandez’s form for Chelsea does not warrant him being handed the captaincy regardless of the recent racism scandal.
‘Can I just speak about it for a second? About his performances since coming in,’ the Arsenal legend added.
‘Yes, in the World Cup you have to say he was outstanding. I’ve not seen him kick a ball in anger since then for Chelsea that makes me think this guy will one day be the captain.
‘He’s not putting those kind of performances in, even before the chant stuff. This guy has done nowhere near enough to be the captain of that club.
‘And they make him captain? That tells me everything you need to know about Chelsea.’
Maresca defended his choice of captain after Chelsea’s disappointing 2-0 defeat to Premier League champions Manchester City.
‘Enzo is one of the captains of this team, he is not the only one,’ the new Chelsea boss said. ‘We have Reece [James], we have some more captains.
‘The reason why is I can see his teammates recognise him, like a reference, as a captain, and he was already captain in the preseason when we changed Reece in the game.
‘All of us make mistakes. It’s important to recognise Enzo did a mistake, recognised the mistake and it’s finished.
‘I don’t know about you, but I did some mistakes in the past and I recognised. As a human being, if you do a mistake and you recognise, you are not going to be punished for life.
‘Enzo did a mistake, recognised. For me, he is one of the references and I have nothing to add.’