The Cuban reaction marked its first public confrontation with the United States since the two countries began discussions in December on fully restoring diplomatic relations.
Cuba joins other leftist regional governments in closing ranks with Caracas in the deepening US-Venezuela row.
An official statement published in the island's state-run media called Obama's executive order implementing the sanctions "arbitrary and aggressive."
"Cuba again reiterates its unconditional support and that of our people for the Bolivarian Revolution, the legitimate government of President Nicolas Maduro, and the heroic brotherly people of Venezuela," the statement said.
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Ecuador's Foreign Minister warned yesterday that the Southern American bloc UNASUR would not allow foreign intervention or a coup in Venezuela.
The European Union said today it has no plans to follow the US lead and impose sanctions on Venezuela.
In Caracas, an irate Maduro pushed back against the new sanctions.
Shortly after they were announced he recalled his envoy to Washington and late yesterday he denounced the US action as "the most aggressive, unjust and harmful blow against Venezuela."
Maduro called the sanctions a "rude outburst" from Obama while surrounded by dozens of ministers and military leaders at the presidential palace.
Venezuela's economy is in crisis, with soaring inflation and many basic goods unavailable or out of reach of most pocketbooks on the black market. Maduro has responded by stepping up a crackdown on dissent, arresting opposition figures and frequently speaking of coup plots.