Seven soldiers were injured but President Maduro was taken to safety.
Venezuela, a once-wealthy oil nation, is in the grips of a five-year crisis under President Maduro's socialist government.
The camera then panned to scores of soldiers who started running, before the transmission was cut.
The audio suddenly drops, and Maduro, his wife Cilia Flores, and other officials on the podium peer up at the sky.
Footage of the speech, circulated on social media, showed Maduro delivering a speech before the sound cuts out, and those on the stage duck.More news: Oil prices slip ahead of inventory report
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Mr Rodriguez said the president and his cabinet, who was standing next to him, were not injured.
Drones loaded with explosives were apparently detonated near a military event in Caracas where Maduro was speaking at a celebration honoring the 81st anniversary of the country's National Guard.
Firefighters near the scene have disputed Mr Rodriguez's version of events.
"We are going to bet for the good of our country", Maduro declared triumphantly. The live television transmission was cut off without explanation. The soldiers lined up in ranks then begin running.
Venezuela's soaring inflation is predicted to top 1 million percent by the end of the year, economists at the International Monetary Fund recently predicted.