The 58-year-old guitarist - who joined the band in 1988 - revealed he started experiencing symptoms "a number of years ago" and admitted it had been a "struggle every day" but he was doing well and was still able to play music.
In a video posted on Instagram, he explained he had been getting ready for No Doubt's residency at the Sphere in Las Vegas and he wanted to share his health news with fans.
"The last couple of months getting ready for the No Doubt Sphere shows, it's been very fun, looking through old footage and looking at old photographs and relearning old songs ... It's kinda made me think about how grateful I am for the life I've gotten to lead as a musician all these years," Dumont said.
"The other thing I wanted to talk about was my health ... A number of years ago I was experiencing a number of symptoms, I went to my doctor, I went to a neurologist and I did a whole bunch of tests, and I was diagnosed with early-onset Parkinson's disease.
"It's been a struggle. It's a struggle every day ..."
However, he went on to insist he was still able to perform and would be a part of No Doubt's Sphere shows, which kick off on May 6.
"The good news is I can still play music, I can still play guitar and I've been doing really well ... I've just been very inspired by other people who have come out to talk about their health issues on social media, and that sort of thing.
"I think it helps erase some of the stigma, and it raises awareness obviously. And awareness is really important for prevention and for research.
"So that's it I am really excited about the shows, I can't wait to see everybody."
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