Bin Hammam, 62, president of the Asian Football Confederation, was due to stand against incumbent Sepp Blatter in the election to choose the head of world football's governing body at FIFA's Congress in Zurich on Wednesday.
Blatter and Jack Warner, the president of CONCACAF, who has also been implicated in the bribery allegations, are also due to face the Ethics Committee on Sunday.
In his statement, Bin Hammam said: "I made the decision to run for the FIFA presidency because I was and remain committed to change within FIFA.
"I set out my goals and ambitions clearly - to further the cause of democracy within FIFA through a commitment to transparency and accountability; through a commitment to expand the number of officials and nations involved in decision-making processes.
"In addition to this, I wanted to spark a debate about change in FIFA. For the good of football, I wanted the future to be bright for our world's governing body and for it to adapt to the ever-changing world we live in today.
"However, recent events have left me hurt and disappointed - on a professional and personal level.
"It saddens me that standing up for the causes that I believed in has come at a great price - the degradation of FIFA's reputation. This is not what I had in mind for FIFA and this is unacceptable.
"I cannot allow the name that I loved to be dragged more and more in the mud because of competition between two individuals.
"The game itself and the people who love it around the world must come first.
"It is for this reason that I announce my withdrawal from the presidential election.
ONE CANDIDATE
With Bin Hammam now out of the presidential race, Blatter should be re-elected as president for a fourth term by acclamation of the 208-member Congress, but that is by no means certain and depends on what happens on Sunday.
Warner, head of the confederation for North and Central America and the Caribbean, predicted in his native Trinidad & Tobago on Saturday that a "football tsunami" was about to strike football's beleaguered world governing body.
All three men are being probed over a report by another FIFA Executive Committee member, Chuck Blazer of the United States, relating to a meeting between Caribbean officials, Warner and Bin Hammam in Port of Spain earlier this month, linked to the election campaign.
The report said there had been possible violations of the FIFA ethics code including "bribery allegations."
Bin Hammam and Warner have denied wrongdoing and Blatter said "the facts will speak for themselves."
In his statement on Saturday, Bin Hammam added: "I will not put my personal ambition ahead of FIFA's dignity and integrity.
"Besides, I believe my candidacy has been a catalyst for debate within FIFA and has brought change to the top of the agenda.
"I pray that my withdrawal will not be tied to the investigation held by the FIFA Ethics Committee as I will appear before the Ethics Committee to clear my name from the baseless allegations that have been made against me."
He continued: "I promise those who stood by me that I will walk with my head held high and will continue to fight for the good of the game.
"I would like to offer my thanks and appreciation to all Member Associations and individuals who supported me. I hope that they will not receive my decision with disappointment and frustration.
"I have a special thank you to my friend and colleague Jack Warner for his unlimited support. I am sorry to see that he has to suffer because of me, but I am promising him that I will be with him all the way through thick and thin.
"I look forward
