Khan, who represents Okhla, was presented in the court after the expiry of his one day police custody.
The 35-year-old woman had filed a complaint against Khan on July 20 for threatening her with dire consequences.
A case was registered against the legislator under Sections 308 (attempt to commit culpable homicide), 506 (punishment for criminal intimidation), 509 (word, gesture or act intended to insult the modesty of a woman) and 34 (common intention) of the Indian Penal Code at the Jamia Nagar police station in south Delhi on July 20.
Police arrested Khan on Sunday.
Khan filed a counter-case on Saturday and claimed he was not even in Delhi when he is alleged to have threatened the woman.
The AAP released a secretly shot video of the woman on Saturday, wherein she is allegedly heard saying she was told by the Station House Officer concerned to level rape charges against Khan.