The president was speaking at a military event in Caracas when the alleged attack occurred.
Live footage of Nicolas Maduro’s speech shows him suddenly looking upwards – startled – and dozens of soldiers running away.
He has blamed Colombia for the attack – something denied by Bogota as a “baseless” accusation.
According to authorities, 7 soldiers were injured, and several people were later arrested.
The incident happened when President Maduro was speaking at an event to mark the 81st anniversary of the national army.
Two drones loaded with explosives went off near President Maduro’s stand, Communications Minister Jorge Rodriguez said.
The president later said in a national address: “A flying object exploded near me, a big explosion. Seconds later there was a second explosion.”
Photos on social media showed bodyguards protecting the president with bulletproof shields after the alleged attack.
Nicolas Maduro accused neighboring Colombia and elements within the US of instigating “a right-wing plot” to kill him.
The president added that he had “no doubt” Colombian President Juan Manuel Santos was “behind this attack”.
Nicolas Maduro, who has previously accused the US of plotting against him, provided no evidence to back his claim.
The Colombian government has denied any involvement, saying there is “no basis” to President Maduro’s allegations.
By contrast, Jorge Rodriguez accused Venezuela’s right-wing opposition of carrying out the attack.
He said: “After losing the vote, they failed again.”
The communications minister was referring to May’s presidential elections, where Nicolas Maduro was re-elected for another six-year term.
Meanwhile, a little-known group called Soldiers in T-shirts said on social media that it was behind the alleged attack.
The group said it had planned to fly two explosives-laden drones at Nicolas Maduro, but they were shot down by the military.
The claim was not backed up by any evidence, and the group did not respond to media requests for comment.
To add further to the confusion, firefighters at the scene disputed the government’s version of events, the AP reports.
Speaking on condition of anonymity, three of the firefighters said the incident was actually a gas tank explosion inside an apartment, but did not provide further details, the AP says.
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