The commission will announce the results of the voting during a press conference on Tuesday evening, the Mena news agency reported late on Monday.
Earlier, electoral commission official Mohamed el-Tanobly had told AFP that the results would not be released until officials could show that the voting "really reflects the will of the Egyptian people."
The National Salvation Front opposition coalition warned that, regardless of the outcome, "the referendum is not the end of the road. It is only one battle."
That raised the prospect of more protests like the ones which have confronted Morsi for more than a month, leaving the Arab world's most populous nation polarised and its political institutions paralysed.
Clashes on December 5 outside Morsi's Cairo palace killed eight people and wounded hundreds, prompting the army to deploy troops and tanks.
Rating agency Standard and Poor's on Monday downgraded Egypt's long-term credit rating one notch to 'B-' and said it could be cut further if foreign exchange reserves or the government's deficit sharply worsen.
"We expect political tensions to remain elevated, with no clear indication that rival factions will be brought to a point at which they can contribute to addressing Egypt's economic, fiscal, and external challenges," the agency said.
Agreement on a $4.8 billion loan from the International Monetary Fund was put on hold this month, accentuating the risk of Egypt's currency collapsing.
The central bank has run through more than half its foreign reserves since the ouster of longtime president Hosni Mubarak early last year, leaving less than $15 billion.
Egypt's economy, once a vibrant opportunity for investors, was brought low by the 2011 revolution and has continued to lag under Morsi.
It was unclear how a political remedy could be reached.
Morsi and the Muslim Brotherhood are using their newfound power to spearhead rapid changes they contend will put Egypt on the path to stability.
But the largely urban, liberal, leftwing, Christian and secular opposition feels alienated by Morsi's steamrolling tactics, and worries the new charter will open the door to strict Islamic law, or sharia.
Merzek, a 29-year-old health ministry employee in the city of Minya south of Cairo who declined to give his last name, said the Islamists "say they want to apply sharia even on Christians. If that happens, we can't say no, but I will stay in my country because, if we go, Egypt is finished."
His wife, Mariane, 25, added: "If they try to force the (Islamic) headscarf on us, I will certainly not wear it."
The direction has also generated international unease.
Germany is echoing the opposition's call for an investigation into the alleged voting fraud.
The United States, which provides Egypt's powerful military with $1.3 billion in aid per year, has kept mostly quiet on the turmoil buffeting its key Middle East ally.
But the Republican chairwoman of the Foreign Affairs Committee in the US House of Representatives, Ileana Ros-Lehtinen, called the vote "a defeat for the Egyptian people" at the hands of "an Islamic dictatorship."
Only Iran, which is trying to claim the Arab Spring was inspired by its own 1979 Islamic revolution, welcomed the referendum. It said it promoted "progressive, Islamic and revolutionary goals" in Egypt.