State security prosecution officials said authorities were questioning Mona Mahmud Mohammad, who was named in the BBC report as "Um Zubeida", or the mother of Zubeida.
She is being investigated over accusations that she had spread false news and for joining an organisation set up illegally, they said.
The mother was arrested on Wednesday.
The BBC report, aired last weekend, referred to the case of a young woman whose mother said she had been the victim of a forced disappearance.
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On Wednesday, the prosecution said it had tasked lawyers with monitoring news outlets and social media to "take necessary measures under the criminal law" against "false statements, news and rumours that harm public safety".
Egypt's State Information Service, which regulates foreign media, has called on the British broadcaster to retract its report or face a government boycott.
A BBC spokesperson, however, said: "We are aware of the reports about this BBC story on Egyptian TV and of the comments of the head of the State Information Service. We stand by the integrity of our reporting teams."
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