A member of Morsi's defense team said family members attended funeral prayers in the mosque of Cairo's Tora prison, which was followed by the burial at a cemetery in the Egyptian capital's eastern district of Nasr City.
A statement by Egypt's chief prosecutor said he addressed the court for five minutes before he collapsed.
Morsi's Brotherhood accused the government of "assassinating" him through years of poor prison conditions.
Morsi was sentenced to 20 years in prison on charges of ordering Brotherhood members to break up a protest against him, resulting in deaths.
A number of residents were detained, a security source said.
Former Egyptian President Mohammad Morsi, who was ousted in 2013 by the military, died Monday after fainting in a courtroom.
Turkey's President Recep Tayyip Erdogan offered his condolences. "This makes it all the more crucial for the authorities to carry out an investigation to determine whether any such ill-treatment was a contributing factor to Mohamed Morsi's death, and ensuring that those responsible for the violation of his rights are held accountable", Amnesty International said on Monday.
Adaylah noted that the Islamic Action Front would instead accept condolences over Morsi's death on Tuesday at the headquarters of the group's general secretariat.
Morsi's death is likely to increase worldwide pressure on the government over its human rights record, especially conditions in prisons. Afterwords he was buried, in a ceremony only attended by family members, under heavy security.
The Palestinian Islamist group Hamas said Mursi had "served Egypt and the (Muslim) nation and the Palestinian cause".
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Rights groups called for an independent probe into the detention conditions and death of the Islamist, who was ousted in 2013 after a year of divisive rule.
Egyptian newspapers have largely avoided covering the story in depth, but thanks to Twitter and Facebook Morsi's family were able to get their voices out.
Al Raissouni also accused Saudi Arabia and the UAE of killing innocent people in Egypt, Libya, Yemen, Sudan and other Muslims.
Mursi was elected to power in 2012 in Egypt's first free presidential election, having been thrown into the race at the last moment by the disqualification on a technicality of millionaire businessman Khairat al-Shater, by far the Brotherhood's preferred choice.
"The Islamic Republic of Iran, while respecting the views of the great and courageous nation of Egypt, offers its sympathies over the death of Dr. Mohamed Morsi to the Egyptian people, his family and his loved ones, and asks God to bestow His mercy and blessings on him", the spokesman said.
Above all, Hamas added, Morsi served the Palestinian cause, which he supported at all regional and global levels, not to mention his efforts to defend Jerusalem and Al-Aqsa Mosque when he was a member of the Egyptian parliament.
The SIS added that the June 2017 HRW report contradicted an official report that was issued simultaneously which stated that Morsi was in good health and only suffered from diabetes.
Egypt's state information service later said Whitson's statements were "nothing but false claims" that reaffirm what it called HRW's tradition of "circulating lies".
Other Brotherhood leaders have also died in custody.
The anger was not directed at Sisi alone, with many blaming western states for supporting him and also criticising western media outlets for downplaying Morsi's death.