Krajicek, from Holland, was a contender for the role with the organisation which runs the men's tour.
American Adam Helfant will stand down as chief executive at the end of the year, creating the vacancy.
Dutch newspaper De Telegraaf reported 40-year-old Krajicek withdrew his name because he felt he lacked the required support to land the job.
Krajicek told the newspaper: "Of course it is disappointing that I had to take this decision. I would have been very happy to become the new CEO of the ATP tour."
The 1996 Wimbledon champion is director of the ABN AMRO World Tennis Tournament in Rotterdam.