inciting violence and ruining the economy.
61-year-old Morsi, Egypt's first democratically elected President, was toppled by the powerful military early this month and since has been kept under detention along with some senior aides of his Muslim Brotherhood party.
Morsi was last seen in public on June 26 and has been held at an undisclosed location.
In a statement, the public prosecutor's office said it had received complaints against Morsi and eight other Islamist figures including Muslim Brotherhood's leader Mohamed Badie. It did not identify other Islamist leaders.
The military maintains it deposed Morsi in a justified response to popular demand after millions of people demonstrated against him. The Brotherhood claims it was a coup that reversed democracy.
Complaints such as those against Morsi are a first step in the criminal process, allowing prosecutors to begin an investigation that can lead to charges.
Announcing the step was unusual: typically prosecutors wait until charges are filed. The prosecutors did not say who had made the complaints.
Egyptian law allows them to investigate complaints from police or any member of the public.
Badie and several other Brotherhood officials already face charges for inciting violence that were announced earlier this week, but few of them have been arrested.
Brotherhood spokesman Gehad El-Haddad said the charges were absurd and that it was the authorities themselves that were responsible for inciting violence.
"They execute the crime themselves and then they slap it on their opponents. As long as you have a criminal police force and a complicit judiciary, the evidence will appear and the judge will be satisfied. And the media will sell it to the public," he said.
Morsi's Brotherhood party on Saturday called for more mass demonstrations after a huge march broke up peacefully before dawn, ending a week in which at least 90 people were killed.
The Brotherhood, which has maintained a vigil near a Cairo mosque since before the army removed Morsi on July 3, has said it will not leave until he is restored to power.
Tens of thousands had turned out on Friday for what the Brotherhood called a "day of marching on". Large crowds of Brotherhood supporters finally dispersed early on Saturday.
Morsi's opponents say those demonstrations are still much smaller than the ones that brought him down.
However, the Brotherhood has shown its organizational muscle by keeping its vigil running into a third week and bringing in coach loads of supporters from the provinces during the Ramadan fasting month.
Senior Brotherhood figure Essam el-Erian, one of those who faces arrest, called on his Facebook page for more demonstrations on Monday.