The 67-year-old had just addressed the court, speaking from the glass cage he is kept in during sessions and warning that he had “many secrets” he could reveal, a judicial official said.
A few minutes afterwards he collapsed, the official said.
State TV said Mr Morsi died before he could be taken to hospital.
Mr Morsi has been in prison undergoing multiple trials ever since the military ousted him in July 2013 and launched a massive crackdown on his Muslim Brotherhood and other Islamists.
Monday’s session was part of a retrial, being held inside Cairo’s Tura Prison, on charges of espionage with the Palestinian Hamas militant group.
Mr Morsi’s son Ahmed confirmed the death of his father in a Facebook post.
Mohammed Sudan, a leading member of the Muslim Brotherhood in London, described Mr Morsi’s death as “premeditated murder”, saying that the former president was banned from receiving medicine or visits and there was little information about his health condition.
“He has been placed behind a glass cage (during trials). No one can hear him or know what is happening to him. He hasn’t received any visits for a months or nearly a year. He complained before that he doesn’t get his medicine. This is premeditated murder. This is slow death.”
The judicial official said Mr Morsi had asked to speak to the court during the session.
The judge permitted it, and Mr Morsi gave a speech saying he had “many secrets” that, if he told them, he would be released, but he added that he was not telling them because it would harm Egypt’s national security.
Mr Morsi was a longtime senior figure in Egypt’s most powerful Islamist group, the Muslim Brotherhood.
He was elected in 2012 in the country’s first free presidential election, held a year after an Arab Spring uprising ousted Egypt’s longtime authoritarian leader Hosni Mubarak.
His Muslim Brotherhood also held a majority in parliament.
The military, led by then-defence minister Abdel-Fattah el-Sissi, ousted Mr Morsi after massive protests against the Brotherhood’s domination of power.
Mr El-Sissi was subsequently elected president and has waged a massive crackdown on Islamists and other opponents since.
Since Mr Morsi’s ousting, Egypt’s government has declared the Brotherhood a terrorist organisation and largely crushed it with a heavy crackdown.
Tens of thousands of Egyptians have been arrested since 2013, mainly Islamists but also secular activists who were behind the 2011 uprising.
He has been sentenced to 20 years after being convicted of ordering Brotherhood members to break up a protest against him, resulting in deaths.
An earlier death sentence was overturned. Multiple cases are still pending.
Mr Morsi was held in a special wing in the sprawling Tora detention complex nicknamed Scorpion Prison.