Watch The Face of Another (1966)

"The Face of Another (他人の顔 Tanin no kao?) is a 1966 Japanese film directed by Hiroshi Teshigahara and based on the novel of the same name written by Kōbō Abe. The story follows an engineer, Okuyama, whose face is severely burnt in an unspecified work-related accident and is given a new face in the form of a lifelike mask."

See more @ Wikipedia

More Info..

1. IMDB
2. Watch on Hulu
3. Trailer: