Khaled Ali is the latest high profile figure to pull out from the 26-28 March elections, making incumbent Abdul Fattah al-Sisi a clear favourite.
On Tuesday, the former chief of staff in the army, Sami Anan, was detained after he put himself forward.
He was accused of violating army rules by running without permission.
President Sisi has been in power since 2013, after leading a military coup that ousted former leader Mohammed Morsi from power, before winning by a landslide in the 2014 presidential election.
He announced his intention to run for a second four-year term on Friday.
How did Mr Ali explain his decision to quit?
At Wednesday's news conference in Cairo, he said: "People's confidence in the possibility of transforming electoral gains into a chance for a new beginning, has unfortunately, in our view, for now ended.
"We announce our decision not to enter this race."
Mr Ali, who never officially submitted his candidacy, said that from the start his intention to run "was met with an angry and irresponsible reaction, manifesting in the arrest of a large number of the campaign's youth".
He also said there was "stubbornness by the electoral commission and many violations".
The commission has so far made no public comments on the latest developments.
It has pledged to ensure the presidential elections will be fair and transparent.
More about: #Egypt