Mr Pincher, MP for Tamworth in Staffordshire, has been Comptroller of the Household since June.
Downing Street said the Conservative politician had also “voluntarily” referred himself to the party’s complaints procedure following allegations about his behaviour.
As a result, he had resigned from the Government to allow an investigation to take place, a spokesman said.
A Downing Street spokesman said: “After several conversations with the Chief Whip, in order to address a number of questions, Mr Pincher has voluntarily referred himself both to the party’s complaints procedure and the police, and has voluntarily stood down from the Whips Office in the meantime.”
The Mail on Sunday reported that Mr Pincher had been accused of making an unwanted pass at a Conservative activist.
Mr Pincher told the newspaper: “If Mr Story has ever felt offended by anything I said then I can only apologise to him.”