"I have now reluctantly decided that I cannot, in good conscience, continue to be the public face of a charity that is changing beyond recognition from the one with which I have been so proud to be associated," she said.
Rowling said she had taken the decision to stand down "with profound sadness and regret" but added that her financial backing for a research project into the disease at Edinburgh University would continue.
She said in a statement: "This disease claimed my mother's life at the age of 45, and I hope to continue giving both time and money to a cause which remains so close to my heart."
Rowling said she had initiated a mediation session last year in a bid to resolve the internal rifts but it had proved fruitless.
Since then, she had "witnessed resignations of immensely dedicated people within MSSS and the increasing demoralisation of staff whom I have come to know and admire over the 10 years of our association."
An MS Society spokesman said the charity was "is in the middle of a governance review to make sure we are properly organised to build on the excellent work we already do."
"J.K. Rowling has been a great patron for the MS Society Scotland for many years. We are sorry she is stepping down and thank her for her good work, and for her continued support for the MS research centre in Edinburgh," the spokeswoman added.
Rowling, 43, has earned 560 million pounds (620 million euros, 820 million dollars) from books about the boy wizard, according to last year's Sunday Times Rich List.
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