The concert planned for June 3 in the world´s most populous Muslim-majority country "will have to be cancelled", national police spokesman Saud Usman Nasution told AFP.[break]
"We will not issue a permit for the Lady Gaga concert in Jakarta," he said.
Indonesia´s hardline Islamic Defenders Front (FPI) had mounted protests in the capital, vowing to intercept the "Poker Face" singer at the airport and ensure she does not enter the country.
"We´re very glad the police stopped this moral destroyer from coming to this country, where we believe in God. Of course we stand against her -- she only wears panties and a bra," FPI Jakarta chairman Habib Salim Alatas told AFP.
"She is very dangerous for our young generation. She has even said herself that she´s the devil´s messenger," he said, apparently taking past remarks out of context, after the FPI had threatened to bring thousands onto the streets.
There was no immediate reaction from Lady Gaga, who has the world´s biggest following on Twitter. But her fans, known as "little monsters", took to social media in their thousands.
Theithooker tweeted: "The only one that needs to be banned is FPI itself. They´re embarrassing this country on a daily basis."
Fans set up a new Twitter hashtag called "#IndonesiaSavesGaga" to try to get the police decision overturned.
But another little monster said: "It´s not a matter of #IndonesiaSavesGaga, it´s more like whether Gaga can save Indonesia."
Big Daddy Productions, the promoters, have already sold more than 50,000 tickets and declined to confirm whether the show, part of Lady Gaga´s "Born This Way Ball" world tour, had been officially cancelled.
Another national police spokesman said the force had "no problem with Lady Gaga" but could not issue a permit without a letter of recommendation from the Jakarta police, who "have decided not to do that".
The Jakarta city police said they had received objections to the show by the National Ulema Council, Indonesia´s top Islamic body.
"The first thing we´ve heard from various public leaders is that Lady Gaga doesn´t deserve the attention of so many people," said Jakarta police spokesman Rikwanto, who goes by one name.
"They said her outfits are too sexy, indulgent and erotic."
Ninety percent of Indonesia´s 240 million people identify themselves as Muslim, but the vast majority practise a moderate form of Islam.
Lady Gaga has faced opposition elsewhere on the Asia leg of her tour.
The Korean Association of Church Communication vowed in March to take "concerted action to stop young people from being infected with homosexuality and pornography" during the US star´s concert in Seoul.
But Lady Gaga has not toned down her performances so far. At shows in Seoul, Hong Kong and Tokyo, she has ridden on to the stage on a mechanical horse, wearing a black bodysuit and an enormous black metal headpiece.
Lady Gaga will perform in Taipei on Thursday and Friday, and will then head to Manila, Bangkok and Singapore. She was due to play in Jakarta after that, before flying south to New Zealand and Australia.
In the past, performers such as Beyonce and the Pussycat Dolls have been allowed to perform in Indonesia provided they dressed more conservatively.
Concerts by Western artists in Indonesia´s fellow Islamic neighbour Malaysia have also stirred controversy. Beyonce was forced to cancel a 2007 event there after conservative Muslim groups threatened protests.
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