The UN General Assembly adopted the annual resolution for the 25th time by an overwhelming vote of 191 votes in favor -- with only the United States and Israel abstaining in the 193-nation forum.
"The United States has always voted against this resolution. Today the United States will abstain," US Ambassador Samantha Power told the assembly, drawing loud applause.
Washington's abstention was in line with calls from President Barack Obama for the opposition-controlled Congress to lift the decades-old embargo as part of a historic normalization of relations.
But restoring full trade and financial ties with Cuba would require legislative action by Congress, where the Republican majority has said human rights concerns must first be addressed.
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Cuban Foreign Minister Bruno Rodriguez welcomed the US shift as positive, but said the US government must take concrete steps that go beyond the "vote of one delegation in this forum."
"The blockade continues to be a massive, flagrant and systematic violation of the human rights of all Cuban men and women and qualifies as an act of genocide," Rodriguez said.
Over the past six decades, the damage from "this genocidal policy" amounts to $753.688 billion, he added.
"There isn't any Cuban family or sector in our country that has not suffered from its effects," said the foreign minister.
Embargo restrictions have prevented the sale of US medical equipment to treat Cubans suffering from Parkinson's disease and blocked a deal by a Cuban pharmaceutical company that would have allowed it to produce drugs locally, he said.
The measure calls on all member states to refrain from applying the embargo and to "reaffirm the freedom of trade and navigation."
Last year, the United States and Israel were the only two countries that voted against the non-binding resolution, but 191 voted in favor -- the highest level of support yet for the measure at the United Nations.
Power recalled that the US policy aimed at isolating Cuba "was not working" and had instead isolated the United States.
After praising Cuba for sending hundreds of doctors to West Africa to fight the Ebola outbreak, Power said the United States and Cuba must continue to find ways to engage, despite differences.
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