The video stars The Walking Dead actor Norman Reed as Judas and was directed by Laurieann Gibson.
In the video, Jesus has long pleated hair and wears an open black leather jacket and a crown of thorns on his head.
It has already come under fire from the Catholic League for Religious and Civil Rights.
Spokesperson Bill Donohue said Lady Gaga was "trying to rip off Christian idolatry to shore up her talentless, mundane and boring performances".
"Is this the only way to jet up her performance?"
But Lady Gaga evidently doesn't see what the fuss is all about.
She told E!: "I don't view the video as a religious statement. I view it as a social statement. I view it as a cultural statement.
"It's a metaphor. It's not meant to be a biblical lesson."
In the song, Gaga sings about being in love with the wrong guy - symbolised by Judas.
Lyrics include: "In the most biblical sense / I am beyond repentance / Fame hooker, prostitute wench, vomits her mind / ... / Jesus is my virtue / Judas is the demon I cling to / I'm just a holy fool, oh baby he's so cruel / But I'm still in love with Judas, baby."
In a recent interview with the Skorpion Show, Gaga said the song was "about constantly walking towards the light in my life, but always clutching onto the light while peering towards the devil in the back".
"I sing about what a holy fool I am, and that although moments in my life are so cruel relationships can be so cruel I'm still in love with Judas. I still go back again to those evil things."