"I want to devote every ounce of my strength and energy to my husband's healing, and to do so it's important for me to dedicate this time to him and to our children," Dion said on her Facebook page.
"I also want to apologize to all my fans everywhere, for inconveniencing them, and I thank them so much for their love and support."
The Asia tour had been scheduled to take place later this year.
Rene, Dion's husband, had a cancerous tumor removed last December.
Since then, "it's been a very difficult and stressful time for the couple as they deal with the day-to-day challenges of fighting this disease while trying to juggle a very active show business schedule, and raise their three young children," the Facebook post said.
It also said the Canadian star has herself been suffering from a condition that caused her throat muscles to become inflamed, forcing her to cancel her scheduled shows in Las Vegas since the end of July.
"She still has not recovered from this condition," the post said.