Willis, 67, rose to fame in the 1980s comedy-drama TV series Moonlighting, and has appeared in about 100 films across his four-decade career, garnering acclaim for his roles in Pulp Fiction and The Sixth Sense, and winning a Golden Globe Award and two Emmys.
But Willis is perhaps best known for playing the tough-as-nails New York cop who pursued bad guys in the five Die Hard movies, released from 1988 to 2013.
"This is a really challenging time for our family and we are so appreciative of your continued love, compassion and support," his family said in a statement on Wednesday.
Willis and actor Demi Moore were one of Hollywood's most high-profile celebrity couples in the 1990s until their divorce in 2000, but they remained close after the break-up. He is currently married to model and actor Emma Heming and is father to a total of five children with both women.
"We are moving through this as a strong family unit, and wanted to bring his fans in because we know how much he means to you, as you do to him," said the statement, which was shared on Instagram by Demi Moore and their daughter Rumer.
Brenda Rapp, a professor of cognitive science at Johns Hopkins University, said aphasia was a disorder most commonly caused by a stroke that could also stem from head trauma or, in rare cases, from neurological disease.
Symptoms varied widely and could affect speech, comprehension and reading ability, Rapp said. In some instances, aphasia can be treated with speech therapy.
Willis had been especially active in recent years. He appeared in eight movies released in 2021 alone, none of which were critically acclaimed.
Larry Gordon, producer of the first Die Hard movie and its 1990 sequel, said he was saddened by the news of Willis' condition, telling the Hollywood Reporter the actor was "the consummate pro and a gutsy guy".
"Grace and guts! Love to you all!," actor Jamie Lee Curtis wrote on Demi Moore's Instagram account.
On social media, his fans shared their feelings of sadness and shock, and many of them paid tribute to Willis.
"His work has meant more to me than I could ever put into words," wrote a fan with the Twitter handle Cody Leach. "If this is in fact the end of your acting career, all I can say is thank you."
Willis has appeared in films grossing more than $US2.5 billion ($A3.3 billion), according to online database IMDB.Â
