Morsi has been separated from his aides and was taken to the defense ministry," said Gehad El-Haddad, a senior Muslim Brotherhood official and son of a top Morsi aide.
Morsi is detained in a military facility with top aides after the army announced his ouster.
"Morsi and the entire presidential team are under house arrest in the Presidential Republican Guards Club," El-Haddad added.
Haddad's father, Essam El-Haddad, widely seen as Morsi's right-hand man, was among those held, he added.
A military spokesman did not respond to requests for confirmation of Morsi's detention, and it was not immediately clear whether the ousted president would later be allowed to leave.
The Egyptian police has also ordered to arrest 300 leaders and members of Mohamed Morsi's Muslim Brotherhood after the army deposed the Islamist president on Wednesday, the website of the official Al-Ahram newspaper reported early Thursday.
The Egyptian army toppled Morsi on Wednesday after a week of protests that killed nearly 50 people as millions took to the streets to demand an end to his turbulent single year of rule.
The announcement, made on state television by Morsi's own defense minister, armed forces chief General Abdel Fattah al-Sisi.
Sisi laid out details of the roadmap for a political transition, saying the Islamist-drafted constitution would be frozen and presidential elections held early, without specifying when.
The armed forces would "remain far away from politics," he stressed.
The army announced that the head of the Supreme Constitutional Court, Adly al-Mansour, a previously little known judge, would become the new leader of transitional government.