"I have activated the entire armed forces to defend the peace," he said in remarks delivered from the Miraflores presidential palace.
Maduro said he has put the military on alert to respond to the alleged assault.
"Sooner or later, we are going to capture that helicopter and those that carried out this terror attack," he declared.
He did not say when the alleged attack is supposed to have occurred, and said no one was injured and that one of the grenades failed to detonate.
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The beleaguered president, who for weeks has been thundering about alleged coup plots against him, said the aircraft was flown by a pilot who worked for his former Interior and Justice minister Miguel Rodriguez Torres, from whom he is now estranged.
Earlier Tuesday, Maduro repeated claims of a US-backed coup attempt and angrily warned President Donald Trump that Venezuela would fight back against such a move.
His comments came a day after he announced the arrests of five opponents he accused of plotting against him to clear the way for a US invasion.
"If Venezuela were dragged into chaos and violence... We would fight," Maduro bellowed in a speech to supporters.
If a coup prevented his side fulfilling his contested reform plans, he said, "we would achieve it by arms."
He said that an armed intervention in his country would spark a crisis that would dwarf those caused by conflicts in the Middle East.
Addressing Trump, he said: "You are responsible for restraining the madness of the Venezuelan right-wing."
Clashes in anti-Maduro protests over the past three months have left 76 people dead, prosecutors say.
The opposition blames Maduro for an economic crisis that has caused shortages of food and medicine in the oil-rich country.
They regularly accuse him of repressing and jailing opponents. Judicial NGO Foro Penal says there are 383 political prisoners in Venezuela.
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