In the song, Lady Gaga uses Judas, the disciple who betrayed Jesus, as a symbol for always "falling in love with the wrong man over and over again" and going "back again to those evil things".
The lyrics say: "In the most Biblical sense/I am beyond repentance/Fame hooker, prostitute wench, vomits her mind."
She appears in the video as Mary Magdalene wearing a black cape and dark make-up.
Bill Donohue, spokesperson for the Catholic League for Religious and Civil Rights, said the video was a "stunt".
"Lady Gaga tries to continue to shock Catholics and Christians in general. She dresses as a nun … she swallows the rosary. She has now morphed into a caricature of herself," he said.
"She is trying to rip off Christian idolatry to shore up her talentless, mundane and boring performances. Another ex-Catholic whose head is turned around.
"Is this the only way to jet up her performance? This isn't random, we are getting closer to Holy Week and Easter. Does she actually believe her own BS?"
Judas is the second single to be released from Lady Gaga's forthcoming album, Born This Way. The first single release, also called Born This Way, was also criticised for its lyrics.
The song says: "I'm beautiful in my way, 'cause God makes no mistakes. I'm on the right track, baby I was born this way."
Jeff Johnston, who works for Christian ministry Focus on the Family and who was formerly gay, said the lyrics contained "bad theology" because they suggested there was no opportunity to reform fallen nature.
"When I was a young adult, this message would have taken away any sense of hope," he said.
"Thankfully, Christianity allows for transformation and freedom from sin."