Justice Minister Patrick Chinamasa said the vote, just three weeks away, "will not be stopped because of lack of money," the state Sunday Mail newspaper reported.
Chinamasa said the financing was "sourced locally" from commercial and business interests after the United Nations and possible outside donors weren't given enough time to contribute.The referendum date was announced a week ago.
The state election commission says it needs $85 million for the vote ahead of national elections later in the year to end the nation's shaky coalition between President Robert Mugabe and the former opposition formed after the violent and disputed elections in 2008.
All coalition leaders have called for a 'Yes' vote on the new constitution.
Finance Minister Tendai Biti said the United Nations citedbureaucratic procedures preventing it from providing referendummoney, adding "we submitted our budgets a bit late,"the Sunday Mail reported.
"I think they are going to fund the actual election but this time (for the referendum) we are going it alone," the paper quoted Biti saying. Biti is the third ranking official in Prime Minister Morgan Tsvangirai's party.
Presidential and parliamentary elections are expected to be held around July.
Rights and democracy groups have called for a postponement of the referendum to give voters more time to study the 160-page draft constitution first published last Monday. They insist a hasty vote will not produce a credible outcome.
Vice President Joice Mujuru said Saturday no Western observers will be allowed into the country to monitor either of the upcoming polls.
Only African and regional observers will be permitted as election monitors, she said while addressing a state funeral in Harare, in the absence of Mugabe, who was on an official trip to West Africa.
Western nations hostile to Mugabe sought to infiltrate the country as monitors to influence the outcome of voting in their favor, Mujuru said.
"Let us be wary of foreign interference in our internal politics," she said.
Mugabe expelled a European Union observer mission during elections in 2002 that the European monitors alleged were marred by violence and vote rigging.
Western donors give the bulk of pledges to United Nations appeals for funds to help member states.
The official election commission says that in a departure from usual election practice the voters' lists will not be used in the March 16 referendum. Voters aged 18 and above can cast their ballots in any of 9,000 polling states across the country using only valid national identity cards.
That procedure would mean a larger voter turnout within the time constraints up to referendum, it says.
In previous parliament and presidential elections, glaring errors in the voters' lists, including registered voters who have long since died or have moved to other districts, were blamed for vote rigging and fraud.