The move follows an announcement by electoral officials that they would be unable to overcome continuing problems with the computerised vote-counting system.
Ivan Rincon, president of the supreme court, said the conditions did not exist that would ensure "credibility and transparency" in the vote.
'Suspending the game'
There are more than 36,000 candidates standing for 6,241 posts. Venezuelans are due to elect the president, assembly members, and local officials.
Speaking to reporters earlier on Thursday, President Hugo Chavez compared the technical glitches to heavy rain before a baseball game.
"The wisest decision by an umpire would be to suspend the game," Mr Chavez said.
US protest
The postponement follows protests from the US and Spanish embassies in Caracas about the treatment of employees of the Nebraska-based company Election System and Software (ES&S) who were sent to sort out the technical problems.
Company employees were allegedly subjected to abuse by secret police, including having guns pointed at their heads, forcing them to seek refuge at their respective embassies.
President Chavez had blamed ES&S for the problems, saying it was part of a wider plan to destabilise Venezuela's electoral process.
ES&S said the thousands of changes made by the election authorities had hindered its work.
Divided nations
The elections are required under a new constitution pushed through by Mr Chavez in 1999 which called for the "re-legitimisation" of many public offices.
A tense political climate has prevailed in the run-up to the election. Correspondents say the country's poor have been pitted against the rich, dividing it as it seldom has been before.
In the presidential race, Mr Chavez is being challenged by former supporter and state governor, Francisco Arias Cardenas.
Mr Arias helped him stage the failed coup of 1992 but broke away from him after accusing the president of betraying the ideals of their rebellion.