Naomi Mutah took part in a meeting called by First Lady Patience Jonathan and was then taken to a police station, they say.
Mrs Jonathan reportedly felt slighted that the mothers of the abducted girls had sent Ms Mutah to the meeting.
Analysts say Mrs Jonathan is a politically powerful figure.
Ms Mutah, a representative of the Chibok community where the girls were seized from their school more than two weeks ago, last week organised a protest in the capital, Abuja.
The protesters, and many Nigerians, feel the government has not done enough to find the missing girls, who are thought to have been kidnapped by militant Islamist group Boko Haram.
Boko Haram has not commented on the accusation.
Pogo Bitrus, another Chibok community leader, told the BBC he had been to the Asokoro police station where Ms Mutah is reported to have been taken but could find no written record of her being there.
He described the detention as “unfortunate” and “insensitive”.
He said he hoped Mrs Jonathan would soon “realise her mistake”.