The 34-year-old's death was announced by his representatives on Monday, according to reports.
Mitte rose to fame in his role as Walter White Jr in the Emmy-winning series, and used his platform to advocate for disability rights from his experience of living with cerebral palsy.
In an emotional Instagram post, Cranston said the pair had exchanged text messages in recent weeks and tried to arrange a catch-up.
"I'm in deep despair as I write this tonight. RJ Mitte, my sweet son on Breaking Bad has died," he wrote.
"I met him when he was only 14 years old when he was cast as Walter White Jr, a part he played with such joy and enthusiasm.
"Born with cerebral palsy, he never - ever - allowed that challenge to be an excuse for anything.
"He met the demanding shooting schedule head on with great determination."
Mitte, real name Roy Frank Mitte III, was an actor and producer who started his career in entertainment playing minor roles in sitcoms such as Everybody Hates Chris and Hannah Montana.
He made a name for himself in 2008 after landing a lead role in hit crime series Breaking Bad, starring as the son of mild-mannered high school chemistry teacher Walter White, who transforms into a ruthless drug kingpin.
Mitte first appeared in the series aged 15 and had a recurring role until its conclusion in 2013, featuring alongside Hollywood stars such as Cranston and Aaron Paul, as well as Anna Gunn, Bob Odenkirk and Dean Norris.
Norris, who played Mitte's uncle and DEA agent Hank Schrader on Breaking Bad, said on social media that "though RJ didn't play my TV son, I always looked out for him as a young kid on set. He was a sweetheart of a young man and will be greatly missed".
Paul, who played drug user turned drug dealer Jesse Pinkman, said in a statement to The Hollywood Reporter: "RJ, I love you my friend. You will be missed. And to whoever happens to be reading this, please know you are loved, and you are not alone. Always remember that."
Mitte also landed TV roles in Switched At Birth, Vegas, Now Apocalypse and Chance, and has featured in films such as Time Share, Dixieland and Westhampton.
During his varied career, Mitte walked the catwalk for a Vivienne Westwood fashion show, and also presented part of Channel 4's coverage of the 2016 Rio Summer Paralympics.
He was diagnosed with cerebral palsy at age three, and was outspoken about his disability and passionate about using his platform as an actor to educate and inform viewers.
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