In a live Q&A on Sunday, Douglas said that Kilmer was "dealing with exactly what I had," referring to his own battle with stage 4 oral cancer.
"Things don't look too good for him," Douglas said.
In a post to Facebook on Tuesday, Kilmer said Douglas' statements were false.
"I love Michael Douglas but he is misinformed," Kilmer wrote, explaining that he hadn't talked to his former co-star for nearly two years.
"The last time I spoke to him was almost two years ago when I asked him for a referral for a specialist to get a diagnosis for a lump in my throat," he explained. "I have no cancer whatsoever."
He went on to thank his fans for their support and said that he was being responsible for his health.
"I hope this puts to rest any further concerns about my health," Kilmer said. "Whatever led Michael Douglas to speculate about my health, he's a loving and devoted friend to privileged group of talent people around the world, and I'm sure he meant no harm."