Ms. Banks, who holds the marginal seat of Chisholm in Melbourne's east, says she felt compelled to speak out, saying she would not tolerate bullying or intimidation.
Her allegations come as concerns are also raised by some Indigenous groups about the appointment of Tony Abbott as special envoy on indigenous affairs.
Liberal MP Julia Banks is quitting politics, saying the leadership crisis that engulfed the party last week was the *"last straw".
Scott Morrison took over as Prime Minister last Friday after a dramatic leadership contest.
In a statement, Ms. Banks says she received hundreds of emails from constituents who wanted Malcolm Turnbull to remain prime minister and Julie Bishop to continue as deputy party leader.
Ms. Banks says she could no longer stay in parliament, offering a very clear statement saying a vindictive, game-playing culture has permeated political life in Australia.
"I have always listened to the people who elected me and put Australia's national interest before internal political games, factional party figures, self-proclaimed power-brokers and certain media personalities who bear vindictive, mean-spirited grudges intent on settling their personal scores."
Ms. Banks says she has experienced harassment and intimidation from within her own party, and from the Labor Party.
She says despite her decision to leave politics, she will continue to fight for gender equality for women in public life and beyond.
"The scourge of cultural and gender bias, bullying and intimidation continue against women in politics, the media, and across the business. Women have suffered in silence for too long and, in the last twelve months, the world has seen many courageous women speak out."
Prime Minister Scott Morrison says Ms. Banks has made an outstanding contribution to the Parliament and has been instrumental in the establishment of the Parliamentary Friends of Women’s Health, and serving as its Chair.
For the moment Mr. Morrison says his first concern is for her welfare and insists bullying won't occur within the party under his watch.
He says he is committed to keeping Australians safe and will continue to consult with colleagues to ensure there can be no question about the culture within the Liberal Party.
"Well, I have no truck with (time for) bullying or intimidation in whatever form it is. I said the other day when it comes to keeping Australians safe - that means everything from what we do on our borders to including when we speak out on things that prevent bullying in the classroom or anywhere else. I am the father of two young daughters and I have no truck with that sort of behavior. One of the things we are moving quickly to do is restore the strong culture in the Liberal Party and bring the party together and show the stability and unity that is necessary, that Australians are looking to me to provide."
Labor leader Bill Shorten says he does not know what Ms. Banks was referring to when she mentioned bullying from the Labor party, adding his party has procedures in place to protect people.
Mr. Shorten says he admires Ms. Bank's professionalism and says her allegations should be taken seriously.
"She is a professional woman, the sort of person you are keen to see take up a political career. So I feel not only the Government's failed by the system has failed if people like her feel they can't continue. In terms of the specific bullying allegations, she's a serious person. She wouldn't have said this lightly. In terms of our own party, we have procedures in place to protect people."
Mathias Cormann, the Liberals' Leader in the Senate, says any potential bullying investigation is a matter for the Liberal Party organization.
