A Turkish pop star who goes by the name Gulsen has been arrested on charges of “inciting hatred and enmity” with a joke she made about Turkey’s religious schools, the country’s state-run news agency reported.

The 46-year-old singer and songwriter, whose full name is Gulsen Colakoglu, was taken away from her home in Istanbul for questioning and formally arrested late Thursday. She was then taken to a prison pending trial.

Amid some speculation that she might be quickly released given her celebrity status, as of Saturday that did not appear to be the case and Ms. Colakoglu was apparently still being detained. Her request to be released from custody pending the outcome of a trial was rejected.

The charges were based on a joke Gulsen made during an April concert in Istanbul, when she quipped that one of her musicians’ “perversion” stemmed from having attended a religious school. A video of the singer’s comment began circulating on social media recently, with a hashtag calling for her arrest.

In remarks reported in the Turkish daily Habertürk on Saturday, Gulsen rejected the accusations of incitement and indicated the barb was an inside joke taken out of context. 

There is a musician in her band named Miraç, she explained, who has the nickname “imam.” 

“We joke with friends as ‘stupid, stupid, perverted’ among ourselves [and] unfortunately, these two words came together.” In a further claim that may prove significant in a trial, the singer said “our friend did not study” in a religious school.

Gulsen — who previously became a target in Islamic circles due to her revealing stage outfits and for unfurling an LGBTQ flag at a concert — apologized for the offense the joke caused but said her comments were seized on by “malicious people” wanting to deepen polarization in the country.

During her questioning by court authorities, Gulsen rejected accusations that she incited hatred and enmity, and said she has “endless respect for the values and sensitivities of my country.”

The arrest sparked outrage on social media. Government critics said the move was an effort by Turkey’s president, Recep Tayyip Erdoğan, to consolidate support from his religious and conservative followers ahead of elections in 10 months.

The leader of Turkey’s main opposition party, Kemal Kilicdaroglu, called on Turkey’s judges and prosecutors to release Gulsen.

“Don’t betray the law and justice; release the artist now,” he wrote on Twitter.

The spokesman for Mr. Erdoğan’s Justice and Development party, known by its Turkish acronym AKP, appeared to defend the decision to arrest the singer, saying “inciting hatred is not an art form.”

“Targeting a segment of society with the allegation of ‘perversion’ and trying to polarize Turkey is a hate crime and a disgrace to humanity,” the AKP spokesman, Omer Celik, tweeted.

Mr. Erdoğan and many members of his Islam-based ruling party are graduates of religious schools, which were originally established to train imams. The number of religious schools in Turkey has increased under Mr. Erdoğan, who has promised to raise a “pious generation.”

Among those calling for Gulsen’s release was another Turkish pop star, Tarkan, best known internationally for the song “Kiss Kiss.”

“Our legal system, which turns a blind eye to corruption, thieves, those who break the law and massacre nature, those who kill animals and those who use religion to polarize society through their bigoted ideas — has arrested Gulsen in one whack,” Tarkan said in a statement posted on Twitter.

After the Istanbul court issued an arrest warrant, Gulden was taken to the Bakırköy Closed Women’s Prison. Photos of the arrival there of the singer, more accustomed to attention from performing on stage, fueled a swirling controversy about judicial overreach in a key NATO-member country already infamous for its abysmal record on human rights and freedom of speech. 

To cite one example among dozens, earlier this year a prominent Turkish TV journalist, Sedef Kabaş, was detained and faced imprisonment for “insulting” Mr. Erdoğan simply for reciting a Turkish proverb: “When the ox comes to the palace, he does not become a king. But the palace becomes a barn.”