IAAF council member Fredericks, also a member of the International Olympic Committee, has left a taskforce helping Russia as it bids to be readmitted to international competition.
His decision comes after French paper Le Monde claimed the former Namibia sprinter received a payment days before voting on the 2016 Olympics host city, allegations he denies.
The IOC is investigating the claims.
"I have decided to step aside from the taskforce so that the integrity of its work is not questioned due to the allegations made against me in Le Monde," said 49-year-old Fredericks.
"It is important that the taskforce's mission is seen as free and fair with no outside influence."
Russia's athletes were banned last year following the McLaren report, which outlined a state-sponsored doping programme.
The IAAF says Fredericks' place on the five-person taskforce has been taken by  IAAF Athletes' Commission chairperson Rozle Prezelj.
Four-time Olympic silver medallist Frankie Fredericks has stepped down from a key role at athletics' world governing body after corruption claims.