The show has been the subject of controversy after a video leaked which showed Minaj shouting at Carey during auditions.
The feud appeared to escalate after Carey allegedly told Barbara Walters that Minaj had threatened to "shoot" her during the altercation, a statement denied by Minaj and executive producer Nigel Lythgoe.
However, Cannon has now told E! Online that he "wasn't concerned" about his wife's safety.
"With drama, it's theatrics," he said. "I'm not worried about that stuff."
Cannon added that he doesn't know whether Minaj did make a gun threat, saying: "I wasn't there. It made for good news. It sounded good, right? Good job, Fox."
The America's Got Talent host has previously hinted that the video could have been leaked as a publicity stunt, saying that he was "disappointed" in the show's network Fox.
Minaj is also said to be angry with the show's producers over the argument, which host Ryan Seacrest previously described as "intense".
Former judge Steven Tyler has also alleged that the altercation was a stunt, but American Idol's bosses recently released a statement insisting that "production is going extremely well".