Angelil had surgery last December to have a cancerous tumour removed.
Dion released a statement Wednesday saying it has been a "difficult and stressful time" trying to fight the disease while raising three young children and balancing her singing career.
She has also been grappling with inflammation in her throat muscles, the statement said, and hasn't been able to perform her scheduled Las Vegas shows since July 29.
All of her performances at the Colosseum at Caesars Palace have been cancelled until further notice. She will also scrap her tour of Asia, scheduled for the fall.
"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," the 46-year-old singer said in a release.
"I also want to apologize to all my fans everywhere, for inconveniencing them, and I thank them so much for their love and support."
In an email to The Canadian Press, a Caesars Palace spokesperson wished Rene a "speedy recovery."
"We are saddened that she has had to cancel her scheduled performances at the Colosseum at Caesars Palace," read the statement.
"Our thoughts are with them and their family and we look forward to Celine's return. Caesars Entertainment is working with AEG Live on potential other bookings for the Colosseum, but it is too early at this time to comment on any specific possibilities."
Angelil discovered Dion when she was 12 years old and has closely shepherded her lengthy career. But in June, it was announced that she'd enlisted a new manager — Quebecor executive Aldo Giampaolo, a "longtime close friend" of the couple.
Dion's most recent album, 2013's "Loved Me Back to Life," topped the chart in Canada before reaching platinum certification four times over.
The lush Colosseum at Caesars Palace was built specifically for Dion, opening March 25, 2003 — the first night of Dion's first residency (the evening was commemorated with a CBS TV special).
That show, "A New Day..." ran for nearly five years. In March 2011, she debuted a new show, simply titled "Celine," which she planned to perform through 2019.
The new show was chosen by USA Today as among the best in Las Vegas, and it's a major draw for Caesars. Pollstar reported that her average show in 2013 brought in more than $657,000 in revenue, while Billboard ranked her as the 23rd highest-earning figure in music in 2013 after she reportedly reeled in $11.8 million for her 60 Vegas performances.
According to numbers provided by Caesars, more than 3.5 million people have bought tickets to see Dion's 928 performances since 2003, amounting to staggering gross ticket sales of $508 million.
In July, Dion said at a Montreal news conference that her husband was doing "really well."
"He's working really hard on his health and he's being a dad at the house, which I'm really happy about."