Speaking on state TV, the 54-year-old president, who has faced three months of opposition protests and some dissent from within government ranks, said that special forces were after the "terrorists" behind the attack.
The helicopter had also flown over the Interior Ministry, he said. "I demand that the MUD (opposition coalition) condemns this eminently coup-mongering attack," Maduro added.
The pro-government Supreme Court is particularly hated by Maduro's opponents for its string of rulings bolstering his power and undermining the opposition-controlled legislature.
Earlier, Venezuela's leader warned that he and supporters would take up arms if his socialist government was violently overthrown by opponents who have been on the streets since April. At least 75 people have died in the unrest.
"I'm telling the world, and I hope the world listens after 90 days of protest, destruction and death," Maduro said then.
"If Venezuela was plunged into chaos and violence and the Bolivarian Revolution destroyed, we would go to combat. We would never give up, and what couldn't be done with votes, we would do with weapons, we would liberate the fatherland with weapons."
Maduro is pushing a July 30 vote for a special super-body called a Constituent Assembly, which could rewrite the national charter and supersede other institutions such as the opposition-controlled congress.
He has touted the assembly as the only way to bring peace to Venezuela. But opponents, who want to bring forward the next presidential election scheduled for late 2018, say it is a sham poll designed purely to keep the socialists in power.
They are boycotting the vote, and protesting daily on the streets to try and have it stopped. Opposition leaders call Maduro a dictator who has wrecked a once-prosperous economy, while he calls them violent coup leaders.
Maduro, who accuses Washington of backing his opponents and seeking to control the nation's oil wealth, said the "destruction" of Venezuela would lead to a huge refugee wave dwarfing the migrant crisis in the Mediterranean.
"Listen, President Donald Trump," he said.
"You would have to build 20 walls in the sea, a wall from Mississippi to Florida, from Florida to New York, it would be crazy ... You have the responsibility: stop the madness of the violent Venezuelan right wing."
Opposition to the July 30 vote has come not just from Venezuelan opposition parties, but also from the chief state prosecutor Luisa Ortega and onetime government heavyweights like former intelligence service boss Miguel Rodriguez.
At a news conference on Tuesday, Rodriguez criticized Maduro for not holding a referendum prior to the Constituent Assembly election, as his predecessor Chavez had done in 1999.
"This is a country without government, this is chaos," he said. "The people are left out ... They (the government) are seeking solutions outside the constitution ... That deepens the crisis."
