The official spoke on condition of anonymity as details of Morsi's detention were not to be made public.
However, Morsi's son Osama later told Qatar-based satellite news channel Al-Jazeera Mubashir Misr that Morsi sent a message to the Egyptian people "to uphold the revolution." A coalition led by Morsi's Muslim Brotherhood planned to hold marches Friday after prayers.
Morsi was toppled in a July 3 coup after millions took to the streets demanding him to step down. He had been held at a secret military facility with no access to outside world, only allowed to make a few short telephone calls to his family.
That changed Monday, when Morsi appeared in public for the first time since the coup at a hearing on charges he incited murder and violence during clashes last year outside the presidential palace. Morsi's family didn't attend the hearing.
"It was just as I expected. He was assuring me and I was assuring him," Morsi's wife said.
Asked if she was worried about his condition, she said: "We didn't waste time discussing these matters."
Morsi spent his first night at Borg el-Arab in a hospital room, complaining of high blood pressure and high blood sugar, officials said.
The Interior Ministry official said Thursday that Morsi spends his time reading the Quran. He also can receive food from outside of the prison and a special medical team monitors his condition.
Meanwhile, Morsi's predecessor Hosni Mubarak could return to prison in mid-November. Prime Minister Hazem el-Beblawi told daily newspaper Al-Masry Al-Youm in an interview published Thursday that Mubarak will return to prison as the country's interim president recently changed Egypt's detention laws.
Mubarak is now under house arrest at a military hospital after being held for two years. Previously under Egyptian law, authorities only could detain prisoners on trial for capital crimes for two years
Mubarak is being retried on charges related to the killing of nearly 900 protesters during 2011 uprising that led to his ouster. He also faces separate charges in corruption cases.
Also Thursday, Egyptian soldiers killed eight militants in clashes in a village called el-Sabkha in the northern Sinai Peninsula, a military official said, speaking on condition of anonymity in line with regulations. The military is fighting Islamic extremists there who have stepped up their attacks since the July coup.