Khan was first detained for questioning and then arrested, a day after he alleged in a press conference that the woman was "pressurised" by police into giving a false statement against him.
"On July 22, the woman had recorded her statement before the magistrate under Section 164 of CrPC. She had alleged while she was returning from the legislator's residence, a vehicle tried mowing her down and Amanatullah was sitting in it," said Joint Commission of Police, Southeast Range, R P Upadhyay.
After her statement to the magistrate, Section 308 (attempt to commit culpable homicide) was added to the FIR, the officer said.
"It is a non-bailable charge and we have arrested Khan," Upadhyay said.
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Reacting to Khan's arrest, Arvind Kejriwal tweeted, "Modi ji arrests one more AAP MLA."
The woman had yesterday filed three police complaints alleging she was receiving threats from unknown persons, following which she has been provided security.
The woman, a resident of Jasola, had last week in a police complaint said she had telephoned Khan on July 10 and later went to his Batla House residence to raise the issue of power cuts with him.
She claimed the MLA did not meet her and while she was returning, a 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.
AAP had yesterday rubbished the allegation levelled against the MLA, claiming Delhi Police had "pressurised" the woman into giving a false statement against Khan.
At a news conference, the party played a video, in which the woman is purportedly seen telling someone "that the SHO of the Jamia Nagar police station asked her to add rape and murder charges in the FIR".
"The woman is in touch with several BJP leaders and she was also taken to the magistrate by a lawyer affiliated to the party.
Khan had further said he has written a complaint to DCP (South-east) of the Delhi Police to file an FIR against the SHO and the woman for "framing" him.