Fabianus Tibo, Marianus Riwu and Dominggus Silva had been due to face a firing squad just after midnight (1700 GMT) on Friday at a secret location in Palu, the capital of Central Sulawesi province.
But Sutanto, the national police chief, said he had received a report from provincial police that the executions "will be after the 17th, not tonight".
The country's national day holiday is on August 17 and police and officials wanted to concentrate on preparing for that, Sutanto said.
The announcement of the delay came after a day of demonstrations against the planned executions by thousands of Indonesians, and a plea by the pope for clemency.
But Sutanto added: "This is only a problem of time. The provincial government will decide the execution timeframe. The fastest would be three days [after the 17th]."
Pope Benedict had called on Indonesia to stop the execution of the three men as thousands of Indonesians held a prayer vigil opposing the death penalty.
Angelo Sodano, the Vatican secretary of state, said on behalf of the pope that clemency should be granted "on humanitarian grounds" for the three men who were found guilty of leading a Christian mob in an attack which killed more than 200 people during Muslim-Christian clashes in the province's Poso region.
Susilo Bambang Yudhoyono, the Indonesian president, had rejected the men's appeals for a pardon last year.
Muslim-Christian clashes raged in Central Sulawesi from late 1998 to 2001, killing 2,000 before a peace accord took effect.
On Thursday, thousands of Christians held a rally in the Poso town of Tentena to oppose the execution.