Earlier, a source in the prosecutors office said Morsi and 198 Islamist leaders and supporters would face a military trial on February 23 over deadly protests that followed his overthrow.
Morsi, an Islamist who was toppled by the army in July 2013, already faces four trials and this would be the first before a military judge.
Military tribunals have been criticised for their harsh and swift verdicts.
State media reported that Morsi would not stand trial on the new charge, explaining that he was already under arrest and cut off from the outside world at the time of the alleged offences.
The case referred to by the prosecution related to protests that broke out in the canal city of Suez on August 14, 2013 in which 31 people were killed.
The demonstrations came on the same day police broke up pro-Morsi protest camps in the capital, during which hundreds of his supporters died in clashes.
At the time, Morsi had been under arrest and incomunicado for more than a month.
The official MENA news agency said Tuesday evening that Morsi and Muslim Brotherhood number two Khairat al-Shater “are not among those charged in the matter of the Suez violence”.
Morsi was Egypt’s first democratically elected leader but his rule was divisive and the army overthrew him after millions of people protested to demand his resignation.
Hundreds of Islamists have since faced mass trials and dozens sentenced to death in a wide-ranging crackdown on the Brotherhood, once Egypt’s largest political movement.
Morsi is already on trial for incitement to murder in connection with clashes outside his palace during his single year in power, and for alleged espionage and collusion with militants to carry out attacks during a 2011 revolt that ousted veteran strongman Hosni Mubarak.
Verdicts in two of the trials, which could result in a death sentence, will be pronounced in April and May.
The constitution allows for military trials of civilians accused of violence against broadly defined military targets, which include public infrastructure such as highways, state universities and bridges.
Military tribunals have been used to sentence dozens of Islamists since Morsi’s ouster, some of them to life in prison.
President Abdel Fattah al-Sisi, the army chief who toppled Morsi and was then elected to office, has pledged to eradicate the Brotherhood, which Egypt now designates as a terrorist group.
Rights groups say more than 20,000 people, mostly alleged Islamists, have been imprisoned.
The government has brushed off international criticism of the crackdown, insisting that the Islamists are violent, while the Brotherhood says it is committed to peaceful protests.