The shock jock made mention of the actors' child just a few months ago during a guest appearance on Shade 45's Rude Jude.
"It irritates the s---t out of me to see someone take that culture and appropriate it," Jude said on-air. "It's like, come on, bro, you're not from that. You learned how to talk from a video, dawg."
Stern agreed and joked, "I understand your point about Chet Haze. He's stealing your black culture."
That didn't sit well with Haze, who took to social media to slam the 61-year-old America's Got Talent judge as well as air his grievances over the increasing criticism he faces as the son of two famous stars.
"Listening to the @HowardStern show this isn't funny at all…Lame yuppie humor #stepyourgameup #outdated."
He continued, "I am a walking PR disaster and I could literally give a f--k less!!!!! People stay telling to chill!!! You're Tom Hanks son!!! Don't be an embarrassment!!! Well guess what… it's my own choice not to give a f--k if my own parents can't motivate me to bite my tongue what the f--k makes you think that you can?"
It should be noted that this isn't the first time Haze has taken aim at the radio star. Back in January, he tweeted, "@HowardStern your time has passed. You're old…Only old people listen to you…The young generation doesn't know you."