His manager, Dennis Varga, said he died on Sunday having been in a coma for several days.
Standing at 2ft 9ins (0.84m), he was billed as the "smallest man in the world" while he worked in the circus before heading to TV.
Alf aired from 1986 to 1990, in which Meszaros wore a full-body suit to portray the titular alien character.
Although the role was voiced by Paul Fusco, Meszaros' diminutive size allowed him to perform in costume, rather than use puppets.
The sitcom followed the friendly alien who crash-landed in the garage of a suburban middle-class family in America.
Born in Budapest, Hungary, Meszaros began his career in his teens, performing in circuses including Ringling Brothers and Barnum & Bailey.
He performed for US Presidents Jimmy Carter and Ronald Reagan and became good friends with Michael Jackson.
He also appeared in films including Big Top Pee-wee, Look Who's Talking and Freaked.
Mr Varga has set up a fund raising page to help pay for Meszaros' funeral costs and medical expenses.
Michu Meszaros, the actor who played Alf in the popular 1980s US sitcom of the same name, has died aged 76.