"Mohamed Naguib al-Tantawi and Mohamed Sayed Ahmed Attiya were arrested on Tuesday evening in Kafr el-Sheikh" in the Nile Delta, human rights activist Hossam Bahgat said.
The pair appeared before the prosecution in Cairo, but the charges against them were not immediately made public, he told AFP.
In March, Ahmed al-Tantawi had announced he was returning to Egypt on May 6 from Lebanon and planned to run for the presidency to offer a "democratic alternative" to the current administration.
Egypt's last presidential election in 2018 saw the incumbent run against a sole opponent, Moussa Ahmed Moussa, a relative unknown who was himself a fervent President Abdel Fattah al-Sisi supporter.
The lawmaker's relatives' arrests come as Egypt launches a national dialogue meant to involve the country's opposition that has largely been decimated since al-Sisi took office in 2014.
At the opening session of the national dialogue Wednesday, veteran diplomat Amr Moussa questioned the "control of security policies over the economy", in apparent reference to the army's chokehold on business sectors.
But critics have denounced the national dialogue as an effort to deflect criticism from abroad over Egypt's rights record.
Though a number of prominent opposition figures have been released from prison over the past year, rights groups estimate that about 60,000 political prisoners remain behind bars.
