Minister Tendai Biti told reporters Wednesday his ministry only has cash for a nationwide census in August and a referendum on a new constitution scheduled around the same time.
President Robert Mugabe has called for elections this year to end a fragile three-year coalition with the former opposition of Prime Minister Morgan Tsvangirai. The coalition was formed in 2009 after disputed and violent elections in 2008.
The finance ministry is controlled by Tsvangirai's Movement for Democratic Change party under the power-sharing deal.
Mugabe has insisted that "money has to be found" for elections to go ahead this year, with or without a new constitution. Tsvangirai says elections can only be held after constitutional and election reforms are complete.
Mugabe, 88, has been nominated by his ZANU-PF party as the sole presidential candidate in the proposed elections.
Biti on Wednesday likened the census and the referendum to elections, in terms of expenditure.
"We have provided money for a referendum and also going to have elections in the form of a census," he said. "So we are going to have two elections. We can't afford a third election."
The finance ministry was this year promised $600 million from the sale of diamonds, but Biti says he has so far received just over $19 million.
"Diamonds have to deliver...we are being crippled by their under-performance," Biti said.
Government employees have embarked on series of strikes this year over pay demands that Biti insists can only be met by improved payments into state coffers from diamond revenues.
Rights groups have also expressed concern that the unaccounted-for diamond revenue could be used by Mugabe's party to finance violence and intimidation in the proposed elections. They have accused diamond mining companies of lacking transparency and accountability in their operations.
Since the military, loyal to Mugabe, took control of the diamond fields in 2008, using troops and helicopter gunships to remove villagers and small-scale miners, Zimbabweans with diamond interests have bought luxury cars and opulent homes.
The boards of the mining companies include executives who are retired and serving police and military officers.