Geneina was an aide to Sami Anan, a former military chief of staff detained after the army accused him of illegally announcing his intention to stand in the March election against President Abdel Fattah al-Sisi.
He was the latest candidate to be sidelined after announcing his intention to run against Sisi, a former army commander who came to power in an election after ousting his Islamist predecessor.
In an interview with HuffPost Arabi published late on Monday, Geneina said the documents, held at a "secure" place abroad, could be released if any harm came to Anan.
Geneinas lawyer Ali Taha told AFP police arrested Geneina at his home and "are supposed to be taking him to military prosecution".
Also Read
The military responded to Geneinas interview with a statement saying it had demanded an investigation against both Geneina and Anan.
In 2016, Geneina was sacked by Sisi as head of the Central Auditing Authority after being accused of exaggerating the cost of corruption in Egypt.
The documents Anan is claimed to have possessed "revolve around political events and crises Egyptian society has passed through" since the January 2011 uprising, Geneina said.
In Egypts first free election in 2012, voters narrowly elected the Muslim Brotherhoods Mohamed Morsi as president.
Anan was armed forces chief of staff from 2005 until 2012 when he and Tantawi were sacked by Morsi, who appointed Sisi to lead the army.
But after a year of divisive rule and mass protests against Morsi, the army overthrew the Islamist in 2013.
Sisi, who was defence minister when Morsi was toppled, was elected president a year later in 2014.
Another rival, the Mubarak-era prime minister Ahmed Shafiq, withdrew from the race after his aides claimed he was deported to Egypt from the United Arab Emirates and held in a hotel.
Shafiq denied in an interview that he had been held against his will.
Yet another potential candidate, military colonel Ahmed Konsowa, was sentenced to six years in prison for illegally announcing his candidacy.
Disclaimer: No Business Standard Journalist was involved in creation of this content