Police arrested Rimsha, who is recognised by a single name, on Thursday after she was reported to be holding in public burnt pages that had Islamic text and Koranic verses on them, a police official said.
A conviction for blasphemy is punishable by death in Pakistan.
The official said that the girl, whom he described as being in her teens, was taken to a police station in the capital Islamabad, where she has been detained since.
Angry Muslim protesters held rallies demanding she be punished, said the official, who requested anonymity because of the sensitivity of the case.
"We had to register the case fairly quickly to prevent any unpleasant situation," he added, referring to the demonstrations.
Rimsha was produced before a court on Friday and remanded in custody for 14 days, another police official said. She is expected to go before the court again by the end of this month.
The girl's plight is likely to reignite debate about growing religious intolerance in Muslim-majority Pakistan, where strict anti-blasphemy laws make defaming Islam or the Prophet Muhammad, or desecrating the Koran, a capital offence.
Human rights activists say the law is often used to settle petty disputes, but in the face of huge public support for the legislation, the government says it has no plans to change it.
The girl's alleged behaviour sparked Muslim anger in Mehrabad, an area of the capital where she lives with her parents and home to up to 800 Christians. Christians there were forced to leave amid mounting fury.
"These Christians had sought shelter with their relatives in other parts of the city but now they are gradually returning to Mehrabad," a senior official of All Pakistan Minorities Alliance (APMA), Tahir Naveed Chaudhry, said.
He said that the girl had Down syndrome - a condition that causes various degrees of learning difficulties - and disputed the age given by police.
"She was just 11 to 12 years old," he said, adding it was a hugely sensitive issue and "we would not like it to be mishandled and would rather want to resolve it amicably".
Women's Action Forum, a leading Pakistani organisation fighting for the rights of women, condemned Rimsha's arrest.
"WAF is outraged at the total inhumanity of the men who lodged the First Information Report in the police," spokeswoman Tahira Abdullah said, demanding Rimsha's immediate release.
Police should have dealt with the case under the Juvenile Justice System and not the serious allegation of blasphemy, she said, accusing police of not allowing lawyers or civil society representatives to visit the girl in custody.