Cole thanked her fans for their support in a statement Tuesday.
"My family and I want to express our extreme appreciation for the outpouring of kindness we have received from all over the country," Cole said.
Cole, 59, also suffers from Hepatitis C.
Cole will spend the rest of the summer recovering before resuming the tour promoting her recent album "Still Unforgettable."
Cole's sister Carole
died the same day that Natalie had her transplant surgery.