The series, which charts the early days of the US's NASA space programme with the Mercury Seven astronauts, only made its debut late last year.
However, Deadline reports that the streamer has decided not to renew it for a second flight – making it Disney+'s first scripted series cancellation.
Studio Warner Bros have decided to shop the series around in the wake of the news, so there still may be hope of a new life on another network such as HBO Max or TNT.
Adapted from Tom Wolfe's 1979 book of the same name, The Right Stuff starred the likes of Suits' Patrick J Adams and Limitless' Jake McDorman, and counted Leonardo DiCaprio as an executive producer.
Colin O'Donoghue (Once Upon a Time), James Lafferty (One Tree Hill), Aaron Staton (Mad Men), Michael Trotter (Underground), Micah Stock (Escape at Dannemora), Nora Zehetner (Grey's Anatomy), Shannon Lucio (The OC) and Eloise Mumford (Chicago Fire) also starred.
The show's official synopsis reads: "At the height of the Cold War in 1959, the Soviet Union dominates the space race. To combat a national sentiment of fear and decline, the U.S. government conceives of NASA’s Project Mercury, igniting a space race with the Soviets and making instant celebrities of a handful of the military’s most accomplished test pilots.
"These individuals, who come to be known as the Mercury Seven, are forged into heroes long before they have achieved a single heroic act. The nation’s best engineers estimate they need several decades to make it into outer space. They are given two years."
The Right Stuff season one is available to stream on Disney+.
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