The move came hours before the 62-year-old Asian Football Confederation chief was due to face an ethics committee hearing into bribery claims.
He said he did not want to see Fifa’s name “dragged more in the mud”.
Mr Bin Hammam had been due to stand against incumbent Fifa chief Sepp Blatter, who is also facing the inquiry. Both deny corruption claims.
Mr Bin Hammam stressed his withdrawal must not “be tied to the investigation held by the Fifa ethics committee”, pledging that he would appear before the panel to clear his name.
His decision not to run means that Mr Blatter is the only remaining candidate in the election of the new Fifa president, scheduled for Wednesday.
The bribery allegations against Mr Bin Hammam stem from a report by Fifa executive committee member Chuck Blazer.
He alleges that the Qatari and Fifa Vice-President Jack Warner jointly organised a special meeting of the Caribbean Football Union (CFU) earlier in May. The meeting was “linked to the upcoming Fifa presidential election”, the organisation said in a statement earlier this week.
CFU members are reported to have told Fifa they were offered sums of cash for “development projects” at the meeting.
In a statement announcing his intention to withdraw from the presidential race, Mr Bin Hammam said he “was and remains committed to change within Fifa” in order to “further the cause of democracy” within the organisation.
But he added that “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.”
The Fifa’s ethics committee hearing is due to start in Zurich, Switzerland, later on Sunday. M
A news conference has been scheduled for 1600 GMT, where the hearing’s outcome could be announced.
Both Mr Bin Hammam and Mr Warner are facing allegations from Chuck Blazer that they offered bribes at the meeting of the Caribbean Football Union (CFU) on 10 and 11 May.
A file of evidence claims bundles of cash of up to $40,000 (£24,200) were handed over to members of the CFU at the meeting in Trinidad.
Both Mr Bin Hammam and Mr Warner deny the allegations.
In turn, Mr Bin Hammam has effectively claimed that Mr Blatter – who is bidding for a fourth term in office – failed to report the payment of alleged bribes, in itself a breach of Fifa’s ethics code.
Mr Blatter, 75, denies any wrongdoing. In a statement on Friday, he said: “I cannot comment on the proceedings that have been opened against me today. The facts will speak for themselves.”
The latest twist in the bitter fight for Fifa presidency follows weeks of damaging headlines and allegations in the wake of the vote for the hosts of the 2018 and 2022 World Cups.
The former was awarded to Russia and the latter to Qatar.