After being filmed arguing with a driver over falling rates, the firm's co-founder and chief executive Travis Kalanick admitted he needed "leadership help". Earlier this month, he announced that the company was looking for a chief operating officer (COO).
The role would have effectively demoted Mr Jones, who was not himself being considered for the position.
In an email to his staff on Sunday, Mr Kalanick said: "After we announced our intention to hire a COO, Jeff came to the tough decision that he doesn't see his future at Uber.
"It is unfortunate that this was announced through the press, but I thought it was important to send all of you an email before providing comment publicly."
The backroom manoeuvrings could suggest bigger changes at Uber are on the way. Two separate, well-placed sources at the company told the BBC that Mr Kalanick could possibly step down as chief executive soon after the new COO is in place - a move that might reassure investors ahead of a long-anticipated potential initial public offering.
A spokesperson for Uber would not comment on the suggestion. However, shortly after this story was published, another source, who also did not want to be named, said there was "zero chance" of Mr Kalanick stepping down when the new COO is announced.