The official state news agency reported voting had started at Egyptian embassies abroad, the same day as the army scheduled talks between rival factions aiming to restore national unity.
Voting on the referendum at home will be spread over two days, December15 and December 22.
The liberal, secular opposition had argued that the chaotic protests and counter protests which followed Morsi's assumption of sweeping new powers late last month meant the referendum should be postponed, but large opposition rallies this week did not change the Islamist president's mind on the matter.
State media said the two-day voting plan had been adopted because many of the judges needed to oversee the vote were staying away in protest at the decision to hold the referendum, so voting had to be staggered to move the judges around.
Morsi was anxious to push through the new constitution as it must be in place before national elections can be held. Those are expected early next year.
In response to the growing political crisis surrounding the referendum, Egypt's military chief will host national unity talks in Cairo later on Wednesday.
Defence Minister Abdel Fattah al-Sisi, who is also the head of the armed forces, said the talks would not be political in character. "We will sit together as Egyptians," he said.
Morsi and the Muslim Brotherhood, which propelled him to the presidency in a June election, were expected to attend, while the main opposition coalition said it would decide on Wednesday morning whether to participate. The opposition stayed away from an earlier reconciliation meeting called by Morsi last weekend.
CRISIS REACHING A HEAD
Outside the presidential palace - where anti-Morsi protesters are demanding the Islamist postpone the vote on a constitution they say does not represent all Egyptians - there was scepticism about the latest round of talks.
The army dominated Egypt throughout the post-colonial era, providing every presidents until Hosni Mubarak was overthrown last year and oppressing the Muslim Brotherhood. After his election, Morsi shunted aside generals who had held interim power after Mubarak and appointed a new high command.
"Talks without the cancellation of the referendum - and a change to the constitution to make it a constitution for all Egyptians and not the Brotherhood - will lead to nothing and will be no more than a media show," said Ahmed Hamdy, a 35-year-old office worker.
But the fact that the army was calling such talks "is an indication to all parties that the crisis is coming to a head and that they need to end it quickly", he said.
Earlier, Finance Minister Mumtaz al-Said disclosed that a $4.8 billion International Monetary Fund loan, a cornerstone of Egypt's economic recovery hopes, would be delayed until next month because of the crisis.
On Tuesday, thousands of opposition supporters had gathered outside the presidential palace to demand that Morsi postpone Saturday's referendum.
A bigger crowd of flag-waving Islamist Morsi backers, who want the vote to go ahead, assembled at two mosques and some remained on the streets through the night. There were also protests in Alexandria and other cities.
The extended upheaval following the fall of Mubarak last year is causing concern in the United States, which has given Cairo billions of dollars in military and other aid since Egypt made peace with Israel in 1979.
State Department spokeswoman Victoria Nuland emphasised "deep concerns" over the situation in Egypt and repeated calls on protesters to demonstrate peacefully and on security forces to act with restraint. She declined to be drawn on whether Washington believed the referendum should be postponed.
The latest unrest has so far claimed seven lives in clashes between the Islamist Muslim Brotherhood and the opposition. But the Republican Guard has yet to use force to keep protesters away from the presidential palace, now ringed with tanks, barbed wire and concrete barricades.