Jorge Arreaza also said his country was a victim of "fake news" that exaggerated its economic difficulties.
The US accuses President Nicolás Maduro's government of violating human rights and subverting democracy.
President Trump's order bans trade in Venezuelan debt and blocks its state oil firm from selling bonds in the US.
Mr Arreaza said that the sanctions and "threats" amounted to "uncivilised politics".
President Maduro would not attend the UN General Assembly in New York next month, he said.
Announcing the new sanctions, the White House said the "Maduro dictatorship" was denying Venezuelans food and medicine.
It said the controversial new constituent assembly - which has voted to take powers from the opposition-led parliament - amounted to a "fundamental break in Venezuela's legitimate constitutional order".
Earlier this month, the US imposed sanctions on President Maduro and some of his closest aides.
Separately on Friday, National Security Adviser HR McMaster said that the US was not planning military action in Venezuela "in the near future".
President Trump had controversially raised that possibility two weeks ago.
Why is Venezuela in crisis?
- More than 120 people have been killed in anti-government protests since April
- President Nicolás Maduro's popularity fell amid attempts to increase his political powers and a deepening economic crisis
- This was compounded by the falling price of oil, which accounts for about 95% of Venezuela's export revenues, and led to cuts to the government's social programmes
- Basic necessities, such as medicine and food, are in short supply
- The opposition accuses Mr Maduro of mismanaging the economy and eroding democratic institutions
- His decision to set up a controversial National Assembly, which was elected in July, sparked nearly daily protests, with opponents labelling it a slide towards dictatorship