A source at the taxi booking app told the BBC the resignation was "completely unexpected".
They said Mr Jones was frustrated the company was hiring a new chief operating officer and that he was not among the candidates.
But according to technology news site Recode, Mr Jones left because of Uber's continued struggle with issues around sexism and sexual harassment.
Uber said in a statement on Sunday: "We want to thank Jeff for his six months at the company and wish him all the best."
Privately, however, the company has been shocked by his sudden departure, with other executives left disappointed at what they saw as a lack of professional courtesy in informing them of his plans.
His resignation will take effect immediately, the BBC understands.
Uber has suffered a spate of controversies in 2017, the most serious being ongoing rows over a culture of sexism, and accusations of sexual harassment at the firm.
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.