According to the Dancing With the Stars judge, at the end of the couple's Dec. 6 Symphony of Dance tour performance in Washington, D.C., Erbert became "disoriented" and was taken to the hospital.
"She was diagnosed with a cranial hematoma from a burst blood vessel and required an emergency craniectomy," Hough wrote on Instagram of the procedure, during which a section of a patient's skull is removed to help ease pressure on their brain. "She is in stable condition."
Hough went on to thank first responders and medical personnel who are looking after Erbert.
"I ask for your prayers," he concluded, "and positivity during this time."
After sharing the health update, fans, friends and fellow stars sent their well-wishes.
"Prayers and love for you both!!!" Jenna Dewan commented, while Brooks Laich wrote, "Sending all my love to you both for a full and speedy recovery!"