As always, he's in good spirits considering the situation," she told People magazine. "We are hopeful that he'll be 100 percent as soon as possible."
Last night, Cannon tweeted that he was being moved from a hospital in Aspen, Colo., where the couple had been vacationing with their twins, Moroccan and Monroe, to a hospital in Los Angeles.
"Currently being [transferred] to a hospital in LA. Thank you all for all your love, prayers and concern," he wrote. "You know me ... I will be a'ight."
"He was transferred to an LA hospital yesterday and is recovering," Cannon's rep told ABCNews.com, declining to go into further detail.
Carey also provided little detail about her husband's diagnosis, but acknowledged to People that "the situation is not easy."
"We are hopeful that he'll be 100 percent as soon as possible," she told the magazine. "We really appreciate everybody's love and support."
The singer made headlines Wednesday when she tweeted that Cannon had been hospitalized: "Please pray for Nick as he's fighting to recover from a mild kidney failure."
Posting a photo of herself lying in a hospital bed with the "America's Got Talent" host, she wrote, "This is us in the hospital -- role reversal; Last year it was me attached to the machines (after having dembabies) and Nick was there with me through it, and now here we are."
"We're trying to be as festive as possible under the circumstances but please keep Nick in your thoughts because this is very painful," she added.
Dr. Giselle Guerra, assistant professor of clinical medicine at the University of Miami's Miller School of Medicine, isn't involved with Cannon's treatment, but said he may have a case of acute kidney failure, also known as acute renal failure.
"Acute kidney failure happens all of sudden, whereas chronic failure happens over time, often as a result of other illnesses like diabetes or high blood pressure," she said. Acute kidney failure can range from mild to serious. Serious cases may require dialysis and may develop into a chronic condition.
There are a number of causes of acute renal failure. In some cases, any damage done to the kidneys is reversible. The condition can be brought on by certain medications or other drugs, an obstruction or something that causes blood flow to the kidneys to drop, such as an infection or dehydration, Guerra explained.
Although she joked about being stranded in Aspen, Carey asked her fans to keep the couple in their thoughts.
"I'm not trying to make light out of the situation because it's a serious moment that's very tough on all of us so please keep us and our family in your prayers. LYM," she tweeted Wednesday.