The promoters had indicated that a deal was being hammered out to tone down the June 3 concert in Jakarta, but the US star's management had stood firm, vowing there would be no compromise to appease religious conservatives.
"Lady Gaga's management has considered the situation minute to minute, and with threats if the concert goes ahead, Lady Gaga's side is calling off the concert," Minola Sebayang, lawyer for promoters Big Daddy, told reporters.
"This is not only about Lady Gaga's security, but extends to those who will be watching her."
The flamboyant performer, who has nearly 25 million followers on Twitter -- the highest number on the social networking site -- wrote just hours before the announcement was made: "There is nothing Holy about hatred."
After the announcement the show was off, thousands of her fans, who call themselves "little monsters", sent a flurry of Twitter messages to persuade her to go ahead with the concert.
Earlier this month Jakarta police refused approval for the show after the Islamic Defenders Front (FPI) threatened violence if Lady Gaga performed, calling her a "devil's messenger" who wears only a "bra and panties".
Big Daddy president director Michael Rusli said it was "unfortunate" that the show, part of Lady Gaga's tour of Asia that drew protests from Christian groups in the Philippines and South Korea, had to be called off.
"For the past few days we have communicated with the government and Lady Gaga's side. The government has given support, but this is not about the permit," he said. "The cancellation is really due to concerns over security."
More than 50,000 tickets had been sold for the event at the Bung Karno Stadium, but FPI Jakarta chairman Habib Salim Alatas said the cancellation was "good news" for Muslims in Indonesia.
"FPI is grateful that she has decided not to come. Indonesians will be protected from sin brought about by this Mother Monster, the destroyer of morals," he told AFP.
"Lady Gaga fans, stop complaining. Repent and stop worshipping the devil. Do you want your lives taken away by God as infidels?"
The FPI has about seven million followers and has been known to raid pubs and clubs.
Lady Gaga is scheduled to play three shows in Singapore this week. She was due to play in Jakarta after that, before flying to New Zealand and Australia, and then to Europe on her "Born This Way Ball" tour.
Indonesian fans had suggested that Big Daddy look for another venue outside the capital after Jakarta police refused to give approval, but Rusli said "this is a huge concert so it can't be moved elsewhere".
"Nowhere else in Indonesia can accommodate that many people", he said, insisting that the 26-year-old singer was "prepared to adapt to Asian culture".
The star's manager Troy Carter said in Singapore on Thursday that Lady Gaga would not tone down her concerts.
Disappointed student Agus Murdadi, 17, said he had been waiting for months to see his idol.
"I'm shocked. She's creative, not provocative. I bought a ticket because I want to see her dancing and singing Judas in front of me," he told AFP.
"I'm going to tweet to her to tell her that she should just come and not worry. The police can take care of FPI. I hate the FPI."
Another fan, Muh Fadli Firdaus, tweeted on @FadliGermanotta: "Sorry for everything, we still love you."
Ninety percent of Indonesia's 240 million people identify themselves as Muslim, making it the world's largest Islamic-majority nation.
In the past, pop stars including Beyonce and The Pussycat Dolls have been allowed to perform in the country on condition they wore more conservative dress than usual.