Rivers, 81, was at a New York City clinic for a throat procedure on her vocal cords when the complications occurred, reports TMZ.
Police tell PEOPLE there was an "81-year-old female transported from a doctor's office on 93rd Street to [Manhattan's] Mount Sinai Hospital in critical condition." By afternoon, her condition was upgraded to stable condition.
"This morning, Joan Rivers was taken to The Mount Sinai Hospital in New York, where she is being attended to," the hospital's spokesman, Sid Dinsay, said in a statement. "Her family wants to thank everybody for their outpouring of love and support. We will provide an update on her condition as it becomes available."
According to reports, the Fashion Police star's daughter, Melissa Rivers, is headed to her mother's side.
Rivers has been as active as ever recently, making headlines last month for walking out on a CNN interview – an incident that David Letterman later jokingly referenced by walking out himself when she appeared on his show.
Rivers promoted her new book, Diary of a Mad Diva, at the New York City Time & Life Building, where PEOPLE is located, on Wednesday.