The "Super Bass" hitmaker was marking the one-year anniversary of her "Queen Radio" broadcasts on Beats 1 when Budden and his The Joe Budden Podcast co-hosts Rory and Mal joined in the fun.
But things got heated when Nicki challenged Joe about comments he made publicly about her rivalry with Cardi B.
Minaj offered up a clip of Budden suggesting she didn't know Cardi would also be appearing on Migos' record "MotorSport".
He took things too far for Nicki's liking when he asked the host if she was on drugs last summer.
"Are you that f**king dumb?" Nicki responded. "You like tearing down women when they can't defend themselves."
Budden's microphone was then cut off and the interview continued with Mal and Rory.
"He's so used to thinking he's the smartest person in the room," Nicki added.
As the awkward chat lit up Twitter, Budden appeared to enjoy all the fuss, writing: "I live for this."
Minaj ended her one-year "Queen Radio" anniversary with another shocker, telling fans that she and her boyfriend, Kenneth Petty, would be getting married within the next 90 days.