The country's foreign ministry called Trump's comments "another extravagant, illegal and unjustified aggression against the Venezuelan people".
The US does not legally have the authority to close another country's airspace, but Trump's online post could lead to travel uncertainty and deter airlines from operating there.
The US has been building its military presence in the Caribbean, which officials say is to combat drug smuggling. Venezuela's President Nicolás Maduro has dismissed US claims of drug trafficking as an attempt to oust him.
In a post on Truth Social, Trump wrote: "To all Airlines, Pilots, Drug Dealers, and Human Traffickers, please consider THE AIRSPACE ABOVE AND SURROUNDING VENEZUELA TO BE CLOSED IN ITS ENTIRETY."
The White House did not immediately respond to the BBC's request for comment.
Trump's comments come days after the US Federal Aviation Administration (FAA) warned airlines of "heightened military activity in and around Venezuela".
In a statement on Saturday, Venezuela's foreign ministry said that the US had "unilaterally suspended" its weekly migrant repatriation flights.
"We call directly on the international community, the sovereign governments of the world, the UN, and the relevant multilateral organizations to firmly reject this immoral act of aggression," it said.
Venezuela on Wednesday banned six major international airlines – Iberia, TAP Portugal, Gol, Latam, Avianca and Turkish Airlines – from landing there after they failed to meet a 48-hour deadline to resume flights.
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