He has been in hospital in the Red Sea resort of Sharm el-Sheikh since falling ill during questioning about corruption allegations and protesters' deaths.
Prosecutors said the 82-year-old was supposed to go to Tora prison hospital, but it was not ready to receive him.
The military council that took power in February is under pressure to try him.
Mr Mubarak's two sons, Gamal and Alaa, along with a number of senior officials and business figures close to him are already being held at Tora prison.
For the past two weeks, the former leader has been in a private wing of a hospital in Sharm el-Sheikh after being admitted with heart problems.
But the public prosecutor, Abdul Maguid Mahmoud, said Mr Mubarak was now fit enough to be transferred to the Mazraa hospital at Tora prison.
He will first be moved to a military hospital in the capital, the International Medical Centre, and then to the prison hospital once proper preparations have been made. The facility is not equipped with intensive care facilities that could deal with any sudden deterioration of his heart condition.
Once there, Mr Mubarak will face questioning over allegations of corruption, including charges that his government supplied gas to Israel at below market prices.
He will also be questioned about his role in ordering the violent response to anti-government protests, in which more than 800 people died.
The prosecutor's office cited a doctor's report as saying Mr Mubarak could be moved without endangering his health, as long as he was given appropriate medical treatment.
An official source cited by the state news agency Mena said he could be transferred to the military hospital with 48 hours.
The BBC's Jonathan Head in Cairo says many Egyptians doubted that the country's new military rulers would be willing to hold the man many soldiers regard as a war hero to account for the abuses of the old regime.
But the incarceration of his sons, many of his closest associates and now Mr Mubarak himself may push those doubts aside, he adds.