The couple, who also have a baby boy Elias, took to Michael's Facebook to confirm the news.
The statement read: "We are devastated about the recent cancer diagnosis of our oldest son Noah who is currently undergoing treatment in the US. We have always been very vocal about the importance of family and the love we have for our children.
Michael and Luisana with their three-year-old son Noah and baby Elias
"Luisana and I have put our careers on hold in order to devote all our time and attention to helping Noah get well. At this difficult time, we ask only for your prayers and respect for our privacy.
"We have a long journey in front of us and hope that with the support of family, friends and fans around the world, we will win this battle, God willing."
Michael, 41, has been rehearsing for his tour next year. On his official website, there are no scheduled dates of his upcoming appearances.
"We are devastated by the recent cancer diagnosis of our son Noah," wrote Michael
Various media outlets reported the news hours before the official statement, claiming that Michael and his Buenos Aires-born wife Luisana were going to make an announcement.
The couple welcomed little Noah in August 2013. Their second son Elias was born in January of this year.
The singer and the model regularly share photos of their adorable brood and it's clear to see how much they love them.
The parents are dedicating their time to taking care of little Noah
Michael has previously spoken about his regret at not having children earlier. He said on Loose Women: "The only regret that I have in my life is that I took this long to have kids, because I had no idea the perspective it would give me. I had no idea how much I would love being a dad. That's it, that's all I care about... I love them too much probably, if there was such a thing.
"It's made everything else so insignificant, moments that I was afraid of and moments that would overwhelm me have now become a joy because I've realised how not serious they are compared to what is really important, which is Noah and Eli and that's it."