According to two senior members of the Muslim Brotherhood, 61-year-old Morsi is being held at a military facility with top aides, media reports said today.
Earlier security forces had imposed a travel ban on Morsi and other leading figures in the Muslim Brotherhood.
The Egyptian police said it has orders to arrest 300 leaders and members of Morsi's Muslim Brotherhood.
The head of Egypt's armed forces yesterday ousted Morsi just one year after he was elected as the country's first democratically elected president in 2012 after nearly three-decades authoritarian rule of strongman Hosni Mubarak.
Egyptian army commander General Abdel Fattah Sisi on state television issued a declaration suspending the Constitution and appointing the head of the Supreme Constitutional Court, Adly Mansour, as interim head of state.
Mansour would be sworn in today, Al-Ahram online reported. Sisi called for presidential and parliamentary elections, a panel to review the constitution and a national reconciliation committee. He said the roadmap had been agreed by a range of political groups.
The move came after Islamist leader refused to quit following the end of a 48-hour deadline set by the army to resolve the political crisis that arose after millions of Egyptian demanding his resignation took to the streets.
Egypt's iconic Tahrir Square, the hub of the anti-Morsi protesters -- erupted into into ecstasy as the military announced his outer. However, a statement on Morsi's Facebook page denounced the army move as a "military coup".
"The procedures announced by the general command of the armed forces represents a full coup d'etat that is completely unacceptable," the statement said. In spite of the military's announcement, Morsi's statement stressed that he remains the head of state and the supreme commander of the armed forces.