"Today we announce our decision that we will not run in this race," Ali said at a news conference in Cairo.
Ali, a leftist who was a presidential candidate in 2012, had yet to submit his candidacy for the March 26-28 election.
From the start, he said, "our announcement was met with an angry and irresponsible reaction, manifesting in the arrest of a large number of the campaign's youth," said Ali.
The very short timetable did not allow for a fair climate for all the candidates to be able to gather the needed signatures in time before next Monday's deadline, he said.
The majority of those hoping to challenge incumbent President Abdel Fattah al-Sisi in the election have either ruled themselves out or sentenced to prison in the past few weeks.