The actor's family, including his wife Emma Heming-Willis and ex-wife Demi Moore, announced his condition on Instagram on Wednesday.
Aphasia is "impacting his cognitive abilities", the statement said.
Willis, 67, is best known for playing John McClane in the Die Hard films, which made him a star.
"With much consideration Bruce is stepping away from the career that has meant so much to him," his family wrote in a joint statement. "This is a really challenging time for our family and we are so appreciative of your continued love, compassion and support."