The move, authorised by an executive order under a national emergency declaration, stopped short of specifying tariff rates or singling out any countries whose products could face US tariffs.
Cuba's state-run media shot back shortly after Trump's announcement, warning that the order threatened to paralyse electricity generation, agricultural production, water supply and health services.
"What is the goal? A genocide of the Cuban people," Cuba's government said in a statement on the nightly TV newscast. "All spheres of life will be suffocated by the US government."
Emboldened by the US military's seizure of ousted Venezuelan President Nicolas Maduro in a deadly raid earlier this month, Trump has repeatedly talked of acting against Cuba and pressuring its leadership.
Trump said this week that "Cuba will be failing pretty soon," adding that Venezuela, once the island's top oil supplier, has not recently sent oil or money to Cuba.
Reuters reported last week that Mexico - Cuba's top supplier after Venezuela cut off shipments in December - was also reviewing whether to continue sending oil amid growing fears it could face reprisals from the United States over the policy.
Trump has used tariff threats as a foreign policy tool throughout his second term in office.
Cuba's president, Miguel Diaz-Canel, said this month that Washington had no moral authority to force a deal on Cuba after Trump suggested the Communist-run island should strike an agreement with the US.
Cuba is facing its worst economic crisis since Fidel Castro's 1959 revolution and is struggling with fuel shortages.
with DPA
