Minaj was seen shouting at Carey after a disagreement over a contestant in a video from auditions obtained by TMZ.
"My wife is the strongest and the classiest woman that I've ever met," Cannon said on Access Hollywood.
"If you watch the video, she just maintains her composure like she does. I don't think she's moved by the theatrics and the pageantry of it all. She signed up to do a job to help young people accomplish their dreams and this is like a sidebar. I hope that's not what this show becomes about, the catfights."
Cannon also suggested that the video was leaked as a publicity stunt, saying that he is "disappointed in Fox" and adding: "I believe that the show is solely about a singing competition. That's why America loves these shows, because they want to see people reach a certain goal or win a million dollars or whatever the prize is on all of these shows.
"And then to make it about something that it's not kind of shows that the producers and the network are kind of losing their foot a little bit. If I'm producing a show that's about young people accomplishing dreams, that's what I want the show to be about - not all the side pageantry."
Asked if the fight was about jealousy, Cannon joked: "You read the script [of the argument]!"
He also suggested that Carey is not dwelling on the altercation, saying: "She called me and we were talking about the kids. It wasn't shaking it off, it's like that's work - at the end of the day she's a mom and she's my wife, so we don't sit and go over, 'Oh, this is what happened'. As much as it seems like big news to everybody, we've got diapers to change and kids to raise."
Cannon added: "I think one of her main concerns was, 'I don't want this to take away from what I signed up for. I signed up to be a mentor on a show that is about people accomplishing their dreams and I want to be a guide'. She doesn't even like the word 'judge'; she's like, 'I just want to guide these young people and give them all the experience that I've been given and all the knowledge I've been given about singing'."
Previous reports have claimed that Carey won't be "fazed" by the altercation. Both she and Minaj have now returned to work on American Idol.
The show's host Ryan Seacrest has admitted that the argument between the duo was "intense" but executive producer Nigel Lythgoe denied rumours that Minaj threatened to "shoot" her fellow judge.
Watch the altercation between Mariah Carey and Nicki Minaj during American Idol filming below: