The National Electoral Board (CNE) had been due to deliver its ruling on whether it accepted or rejected an initial petition with 1.8 million signatures endorsing a recall vote against Maduro, whom the opposition accuses of driving Venezuela into economic and political chaos.
Maduro's opponents warn the country faces an explosion of unrest if authorities do not allow a recall referendum this year.
But just after their meeting with the CNE was due to start, opposition spokesman Jesus Torrealba said the electoral authorities had postponed it indefinitely.
The grinding economic crisis has made daily life increasingly difficult for Venezuelans, who face hyperinflation, shortages of food and medicine, daily power outages, the near-paralysis of government offices and violent crime.
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In a sign of the tension gripping the country, hundreds of soldiers and police fired tear gas to break up a relatively small protest by dozens of anti-Maduro demonstrators just before the referendum meeting was suspended.
Rallying to cries of "We are hungry" and "This government is going to fall," the protesters defied the heavy security presence, erecting barricades in the streets and trying to reach the presidential palace.
The opposition accuses electoral authorities of dragging their feet on the referendum process to protect Maduro.
Maduro's camp in turn accuses the opposition of massive fraud in its petition drive.
Even if the CNE eventually accepts the petition submitted on May 2, Maduro's opponents would face a long and winding road to call a referendum.
And they may not get there by the crucial date of January 10 -- four years into the leftist leader's six-year term -- at which point a successful recall vote would no longer trigger new elections but simply pass power to Maduro's vice president.