A service will be held at St Mark’s cathedral, followed by burial at St Bishoy monastery in the Nile Delta.
Shenouda, 88, was the spiritual leader of Egypt’s Copts – who make up 10% of the country’s population – for decades.
Tens of thousands of mourners have paid their respects to the pope, whose body has been on display in the cathedral.
Copts – the Middle East’s largest Christian community – have been given time off work to prepare for Tuesday’s funeral.
A national day of mourning has been declared for the funeral.
Tens of thousands of people queued to see Pope Shenouda in the past two days.
Dressed in embroidered vestments and a golden miter, and holding a gold-tipped staff, his body was laid in a coffin before being placed on a ceremonial throne.
“The holy pope was able to gain the love of even those who held different opinions and I believe this will be a difficult thing to replace,” said a mourner named as Samir.
“But God protects the Church and he will find a suitable patriarch.”
The BBC’s Jon Leyne in Cairo says the massive crowds bear witness to the huge love and respect for Pope Shenouda.
He was seen as a leader who did his best to protect Coptic Christians at a time when Islamism was on the rise, our correspondent says.
But his deep conservatism -including opposition to divorce – was not always popular with younger Christians.
The first challenge for the new leader of the Church will be to reassure Copts of their place in a country whose largest political party is now the Islamist Muslim Brotherhood, our correspondent adds.
There is no timetable yet for the selection of his successor, who will be elected by a conclave of senior bishops.
Tributes have come in from around the world, with Roman Catholic Pope Benedict XVI offering prayers and US President Barack Obama praising Pope Shenouda as an “advocate for tolerance and religious dialogue”.
Egypt’s military rulers expressed the hope on their Facebook page that his wish of “preserving the unity of Egypt and the unity of its social fabric” would be achieved.
And a senior Muslim cleric, the Grand Imam of the prestigious al-Azhar university, Ahmed al-Tayeb, expressed sorrow and said he “greatly remembers his vision towards Jerusalem and its history”.