The group claimed the song "mocks and blasphemes the name and person of the Lord Jesus Christ, who is the central figure of each faithful Christian in the country", Calixto said.
The Islamic Defenders Front (FPI) said it would create havoc if Lady Gaga were allowed to perform in Indonesia, calling her the "devil’s messenger" and warning they were ready to die to stop the concert.
In March the Korean Association of Church Communication vowed to take action to stop young people from being "infected with homosexuality and pornography" during the star’s concert in Seoul.
But the star has so far failed to tone down her performances. In Seoul, Hong Kong and Tokyo, she rode on to the stage on a mechanical horse, wearing a black bodysuit and an enormous black metal headpiece.
After Manila, the tour heads to Bangkok and Singapore. She was due to play in Jakarta after that, before flying south to New Zealand and Australia.