The 52-year-old only arrived at the Eredivisie outfit at the start of the campaign as a replacement for Ronald Koeman, but has cited differences between himself and the club over how to move forward.
"Our ambitions are not very different from each other, but when it comes to the ability to take the final step to the top, we do not agree on how to meet the high expectations that now prevails at Feyenoord," said Rutten.
"Of course I feel that as a disappointment.
"Feyenoord are still a great club. But club management, players and staff are entitled to a clear conclusion from my side."
Under Koeman, Feyenoord finished as Eredivisie runners-up on two occasions and also recorded a third-place finish.
A goalless draw against Utrecht on Sunday left Rutten's side fourth in this season's table, while the club also exited the UEFA Europa League to Roma last week in a tie marred by crowd trouble.
"We were and are satisfied with Fred," said technical director Martin van Geel.
"The club want him to continue, but of course we have to respect that he does not want to.
"It is certainly good that there is clarity about the future. We now have plenty of time to think about his successor."
