The Canadian singer confirmed the diagnosis on his Facebook page and wrote that he and his wife Luisana Lopilato were "devastated".
His son, three-year-old Noah, is already receiving treatment at a hospital in the US.
The couple have a second son, Elias, who is 10-months-old.
The Facebook message reads: "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.
"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."
The announcement comes just a day after Michael Bublé at the BBC was aired on BBC One.
Speaking to Claudia Winkleman about his children on the pre-recorded show, Bublé said: "I just love them so much that part of loving them so much is not giving them everything they want and that is a tough thing for me."
Bublé was raised as a Catholic but now describes himself as agnostic.
His wife, an Argentinian actress, is a practicing Catholic. The couple has been married for five years.