Khan claimed that he was being "framed" and was "tired" of giving "clarifications" on various allegations levelled against him.
"I exposed corruption in the previous government after I became the Chairman of Delhi Waqf Board. But some people are not liking my honesty and spirit of service as they are framing me and my family in fake cases," Khan said in the letter to Delhi Chief Minister Arvind Kejriwal.
"I am tired of giving clarifications on various allegations... I would like to be free from all the responsibilities... I resign from all the posts," Khan wrote.
Later at a press conference here at the Aam Aadmi Party (AAP) office, Khan said that he was being framed just because he was an AAP MLA.
"I now resign from all the party posts and will fight against corruption as a common AAP worker," he announced.
Following a complaint by the spouse of his wife's brother, a FIR was lodged against Khan at the Jamia Nagar police station in south Delhi.
A senior police officer told IANS: "Khan is booked under Section 354 (assault or criminal force to woman with intent to outrage her modesty), Section 509 (word, gesture or act intended to insult the modesty of a woman) Section 506 (criminal intimidation) Section 498 A (relative of husband of a woman subjecting her to cruelty) and criminal conspiracy.
Khan, however, told the media that he was having "no connection with the woman at all".
"This woman had snapped all ties with our family four years back. She had also clarified this in a letter four years back that she had no connection with me and my family. Now today (Saturday) all of a sudden a case is registered against me on the basis of a baseless complaint from this woman," he said.
He added that police was "targeting" him because he was an AAP MLA but "police never took such swift action against Bharatiya Janata Party (BJP) leaders," he added.
In another case, he was arrested on charges of threatening a woman on July 24 but released on bail on July 28.
Khan, who was made the Chairman of Delhi Waqf Board in March, was recently accused of involvement in an alleged recruitment scam there and the Anti-Corruption Branch (ACB) has launched a "preliminary inquiry" against him.
Khan, however, claimed that the charges against him were baseless.
MLA from Okhla, he raised in the assembly the issue of the previous government illegally giving Waqf Board land to the Delhi Development Authority.
It was learnt from AAP sources that his resignation has not yet been accepted.