"The AAP MLA has been detained for questioning in connection with the matter," said a senior police official.
The woman, a resident of Jasola, had last week in a police complaint said she had telephoned Amantullah on July 10 and later went to his Batla House residence to raise the issue of power cuts with him.
She claimed the minister did not meet her and while she was returning, the youth came out of the house, abused her and threatened that she would be killed if she did not stop politicising the matter.
Amanatullah had, however, said he did not even know if the woman came to his residence.