The comedian, who appeared to be slurring his words on Wednesday's show, explained that he had a problem with his throat.
"My throat specialist feared I had cancer," he said. "I spent three weeks in agony in hospital. It turned out I had a virulent throat infection and I'm now OK. It was disappointing the BBC would not give an explanation."
A spokesperson for the BBC this week disclosed details of the 56-year-old's condition as concerns about his health grew.
"Mel did it for a charity and didn't want to let [viewers] down, despite not being well," said the representative.