The transgender activist star died on Sunday morning, reports BBC.
Her other brother Richmond confirmed the news on Facebook with a press release written by Patricia.
He said Arquette died while listening to David Bowie's music.
Alexis Arquette appeared in films including Pulp Fiction and The Wedding Singer.
Arquette made her film debut in Down And Out In Beverly Hills in 1986 and went on to play a transvestite in Last Exit To Brooklyn in 1989.
She also appeared in The Wedding Singer as a member of a band, impersonating pop star Boy George.
Boy George tweeted: "R.I.P my sister Alexis Arquette. Another bright light gone out far too soon. Love to the family and all that loved Alexis."
Alexis Arquette also appeared in a documentary about transitioning to becoming a woman in 2006.
The film, Alexis Arquette: She's My Brother, screened at the Tribeca Film Festival in 2007.
She also appeared on TV shows including Friends and Californication, and went on to become an activist for transgender rights.