McQueen got his big break in 1984 when he was cast in the hit movie "The Karate Kid," in which he played Dutch, the adversary of Ralph Macchio's lead character.
His attorney, Arthur H. Barens, told The Associated Press that he died on Wednesday.
McQueen followed in his father's footsteps, both on screen and on the motor racing circuit.
His wife, Jeanie Galbraith, posted a tribute to him on Instagram, together, with their son Chase, and daughter, Madison.
The family announced his death "with a heavy heart," adding: "His remarkable journey as a loving father to us, along with his unwavering commitment to our mother, truly exemplified a life filled with love and dedication. His passion for racing not only highlighted his exceptional talent, but also served as a way to honor his father's legacy, a testament to the values instilled in him. He passed his passion, knowledge and dedication down to us and we will continue not only his legacy but our grandfathers as well."
McQueen is also survived by his son from a former relationship, Steven R. McQueen - an actor, who appeared in "The Vampire Diaries."
Chad McQueen reprised his role in "The Karate Kid" sequel in 1986, as well as several other films, and also produced two documentaries about his father: "I Am Steve McQueen" in 2014 and "Steve McQueen: The Man & Le Mans" the following year.
His father, who shot to fame in the 1960s with action movies "The Magnificent Seven" and "The Great Escape," died in Mexico in 1980 aged just 50, following surgery to remove a tumour.
Besides his acting career, McQueen inherited his father's passion for cars. According to AP, he spent years racing professionally - including in the 24 Hours of Le Mans and the 24 Hours of Daytona races - but suffered a series of injuries as a result.
In 2010, he founded McQueen Racing, which he ran with his children Chase and Madison, creating custom cars and motorcycles and working with the movie industry.
"I didn't find acting fun anymore," McQueen said in a 2005 interview with AP. "So, I decided to give racing a total commitment."
In a separate Instagram post, McQueen's son Chase wrote: "Knowing you're now reunited with the your Dad and Sister brings me some comfort. Until we ride again I love you."
Also paying tribute to him online was Jon Hurwitz, one of the creators of "Cobra Kai," the "Karate Kid" revival that has proven a hit for Netflix.
He said he and his colleagues had met with McQueen to discuss a return to the series. Posting on X, Hurwitz described McQueen as a "Karate Kid legend," adding: "Unfortunately, Chad was unable to join us when it came time to shoot. At the end of the day, it wasn't meant to be. But Dutch will always be remembered as a badass' badass in the Miyagiverse. He kicked ass."
He added: "The fandom mourns a Karate Kid legend today. I'm so grateful I had the honor of spending an afternoon with him. Sending much love and strength to his wonderful family. May Chad rest in peace."