The last man on earth
M
Dogtooth
Water Lilies

The last man on earth
M
Dogtooth

I got a little The Abominable Dr. Phibes vibes from this. Disfigurement going on, guy trying to "right" an accident involving a loved one, has a mysterious female assistant doing some dirty deeds for him

Santa Sangre by Jodorowsky

La Piel que habito !!!!
By Almodovar

"Mill Of The Stone Women" is similar.
Definitely worth a look.

Dario Argento's early 70's Trilogy consisting of "Bird with Crystal Plumage", "Cat O' Nine Tails", and "Four Flies on Gray Velvet", may tweak your interest.

The Last Will of Dr Mabuse (1932)
Franju was influenced by Bunuel and Fritz Lang.
the lifting of the skin from a victim's face, packs the biggest punch since the slicing of the eye in Bunuel's Un chien andalou (An Andalusian Dog, 1928).
__@
-_\<,_ ___(*)/ (*)____ nec spe, nec metu
And yet, the only exciting life is the imaginary one.

Kim Ki-duk's "Time".

Didn't see it mentioned. But Corruption (aka Carnage) from 1968 has a very similar plot.

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The best horror will always be from the early-'60s.
It just will.

Like another user said, Almodovar's The Skin I Live In has many similarities. I thought it was inspired by this movie until I just read that it was based on another book. Still, there's no doubt that there's a strong influence from this film.

There are elements in the film that remind me of The Spiral Staircase by Robert Siodmak.
Keep silent unless what you are going to say is more important than silence.

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Well, the guys have been kindly telling you the similarly themed movies, so I'll share the movies with the same nightmarish yet gorgeous quality with this one:
Nosferatu (1922) & Faust (1926)
by F.W. Murnau.
Vampyr (1932)
by Carl Theodor Dreyer.
Dead of Night (1945)
, a British anthology horror film by 4 different directors.
Black Sunday (1960), Black Sabbath (1963), Kill, BabyKill! (1966), and Lisa & The Devil (1974)
by Mario Bava.
Suspiria (1977), Inferno (1980), and Phenomena (1985)
by Dario Argento.
City of The Living Dead (1980), The Beyond (1981), and The House By The Cemetery (1982)
by Lucio Fulci.
The Church (1989), The Sect (1991), and Cemetery Man (1994)
by Michele Soavi.

My top 5 favorite directors: Kurosawa, Spielberg, Jeunet, Argento, and Gilliam.

It may be a stretch but I'd say Polanski's Repulsion has a somewhat similar tone and atmosphere. Totally different plot, though.

Onibaba

There is Almodovar's 'La Piel Que Habito' (The Skin I Live In). It may sound similar but it's based on a novel called 'Tarantula' by Thierry Jonquet.
Karina Licursi ~

there is another mediocre if not sub-mediocre film that doesn't have the same exact plot but it involves being alive, imprisoned and not knowing what the hell is going to happen to you next. It was called "boxing helena" with Julian Sands and Sherilyn Finn. She has left him for another guy so being a surgeon he tricks her into coming out to his house and then he proceeds to remove her arms and legs in 4 separate operations so she can never escape his home. he puts her in a makeshift box so she can stay upright. creepy but the film on a whole was a real stinker. Peeping Tom has my vote for being slightly better or slightly worse than "Eyes Without a Face".

Some Val Lewton films: I Walked With a Zombie, and especially The Seventh Victim.

You asked about similar films, and this one came to my mind several times while watching "Eyes Without A Face": 1976's "Mansion Of The Doomed." The film is about a young woman who's lost her sight, and her doctor-father's attempts to restore her vision. I would say it's a mediocre film, but there are several similarities to this one.

Blood and Roses (1960) is another French horror film released on the same year, with a simillar melancholic, dreamy tone and its slightly better than "Eyes Without a Face". Both films are in my top 10, btw.
The theater is like a faithful wife. The film is the great adventure, the costly, exacting mistress

Onibaba
Well who are you gonna believe, me or your own eyes?