Boko Haram insurgents, who want to create an Islamic state in Nigeria, stormed a secondary school in the village of Chibok in the north-east of the country on 14 April and took the girls away in lorries.
A source in the presidency said Naomi Mutah Nyadar had been detained over allegations of falsely claiming to be the mother of one of the missing girls.
Nyadar was arrested on Sunday after a meeting she and other campaigners had held with President Goodluck Jonathan's wife, Patience, concerning the girls.
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| Nigerian police arrest protest leader for girls abducted by Boko Haram militants |
"Ms Naomi was arrested yesterday evening," he told Reuters. "We are begging them to save our daughters. Instead of taking steps to rescue them they are jailing us."
The presidency source said: "[Nyadar] was arrested because of impersonation. She claimed that she was one of the girls' mothers, so she's just being questioned by the police."
Abana denied Nyadar had made any such claim.
"They are claiming it is a hoax and that her daughter was not abducted. But when we say 'bring back our daughters' the campaign means it in the broader sense of 'daughters of Nigeria'," Abana said. "They are so clueless."
Nigeria's government is becoming increasingly nervous about security for the World Economic Forum (WEF) for Africa, an annual gathering of the rich and powerful to be held in Abuja this week for the first time.
The girls' abductions have been hugely embarrassing for the government before the WEF, which was supposed to focus attention on the growth potential of Africa's biggest economy but now threatens to be overshadowed.
In a televised media chat late on Sunday, President Jonathan pledged that the girls would soon be found and released, but he admitted he had no idea where they were.
Boko Haram on Monday claimed responsibility for the abductions, AFP reported, citing a video it had obtained. "I abducted your girls," Boko Haram leader Abubakar Shekau said in the video, according to AFP.
