The arrest occurred right before a televised statement from the General Command of the Armed Forces, declaring Anan was in violation of military rules for announcing his candidacy without seeking their approval.
The Armed Forces said Anan's announcement "constituted clear incitement against the armed forces with the intention of driving a wedge between it and the great Egyptian people." The military also accused Anan of forging documents to falsely indicate his military service was terminated.
"All legal measures will be taken against him including his questioning," the statement said.
The arrest was harshly criticized by Anan's staff and supporters. Mostafa Al-Shal, Anan's office manager, claimed that Anan had yet to even submit his candidacy papers to the election committee and had only "expressed his intention to run."
Presidential candidates are required to register with Egypt's National Elections Authority by January 29th, according to state media.
Anan announced last week that he would run against the incumbent President Abdel Fattah el-Sisi in the March elections. Anan declared his candidacy in a video criticizing the current government.
Anan was Chief of Staff of the Armed Forces until 2012, when then-President Mohamed Morsi removed the military's top brass. In the shakeup, Anan was named an advisor to Morsi, and Sisi was promoted to Minister of Defense. Just a year later, Sisi ousted Morsi from power following mass protests and won the presidential elections in 2014.
Anan's arrest is the latest interference faced by presidential hopefuls. After announcing his candidacy from self-imposed exile in the United Arab Emirate, the former Egyptian Prime Minister Ahmed Shafik was returned to Cairo by Emirati authorities. He subsequently withdrew his bid.
Following Shafik's withdrawal, Anan was widely viewed as the most qualified contender in the election. A strong military man with solid credentials, he was also thought to be insulated from obstruction.
His arrest now leaves only one other candidate, Khaled Aly, in the race against President Sisi. However, Aly, a prominent human rights lawyer and activist, is facing a lawsuit that could disqualify him from the race.
"We've reached a state of madness in Egypt," said Al-Shal, the office manager.
Meanwhile, the head of Egypt's National Elections Authority, Lashin Ibrahim, urged authorities to hold the upcoming presidential elections in accordance with the law and internationally recognized standards, the state-run Al-Ahram newspaper reported Tuesday.