Anan's son, Samir, said police had raided the family home late on Tuesday.
Ali, a leftist who was a presidential candidate in 2012, had yet to submit his candidacy for the March 26-28 election.
The last credible challenger to Abdel-Fattah El-Sisi in Egypt's presidential election bowed out on Wednesday, clearing the way for an incumbent who appears more intent on cementing his policies than appeasing any concerns about a fading democracy.
With Mr Anan in detention and the withdrawal from the race last week of Mohammed Anwar Sadat, the last chance for a two man race rests with Khalid Ali, a 45-year-old human rights lawyer scheduled to announce the direction of his candidacy in Cairo on Wednesday evening.
The constitution of Egypt requires that election proceedings shall not begin earlier than 120 days from the date of the end of the current presidential term, which ends on June 8 and the results shall not be announced later than 30 days before the date of the end of the current presidential term. A 10-day candidate registration has started on January 20, while electoral campaigns will kick off on February 24 and the result of the first round will be announced on April 2.
In a televised statement broadcast Saturday, Anan announced his decision to run in elections slated for March.
These include former Armed Forces Colonel Ahmed Konsowa who was detained on charges of "disobeying military orders by expressing his political views" and "committing acts that violate military norms by publishing a video on Facebook announcing his plan to run for the presidency". Unless someone steps forward by Monday, the deadline to enter the race, el-Sissi could be the sole candidate.
Egypt was "hell-bent" on arresting and harassing anyone who stood against Sisi, Amnesty said.
The economy has been hit hard under Sisi as unrest in the country has continued since the Arab Spring-inspired protests ousted Mubarak in 2011, which has crippled the tourism sector.
He had yet to present his papers to the election committee.
On Tuesday evening, Egypt's military prosecutor Mohamed al-Roweiny announced that media coverage on the investigation into the case of Sami Anan's presidential bid and military status has been banned.
A statement by the campaign of former military chief of staff and presidential hopeful Sami Annan says it is suspending its activity indefinitely following a statement by the armed forces listing an array of serious allegations against him.
But the lawyer had faced nearly insurmountable challenges from the start, initially in the form of a court case accusing him of making "an obscene gesture" outside a Cairo court.
Anan is not the first former high-ranking official to be prevented from running against Sisi; former prime minister and air force general Ahmed Shafiq withdrew from the race several weeks ago saying he's the wrong person for the job after facing harsh criticism.
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