Austrian Chancellor Werner Faymann said his government would "prepare and file a complaint at the European Court of Justice" to fight the greenlit project.
The EU's decision was backed up "neither by ecological nor economic reasons" and sets a "negative precedent", he said in a statement.
Austria has no nuclear power stations and strongly supports green energy.
"There is absolutely no legal, moral or environmental justification for turning taxes into guaranteed profits for a nuclear power company whose only legacy will be a pile of radioactive waste," said Greenpeace's EU legal adviser, Andrea Carta.
Sources told AFP that 16 votes, one more than the 15 needed, approved the project in a rare occurrence of a commission decision going to a vote and not made through consensus.
The Hinkley Point C project in Somerset, to be built by France's EDF for €19 billion ($26 billion), is one of the world's most ambitious nuclear deals and is seen as a key boost to the industry.
Even before the plant is built, costs appear to have increased by around 50 percent, with EU commissioners suggesting that the real cost will be closer to £24.5 billion (€31.05 billion).
The decision was controversial, with green critics in Britain saying that the government should have offered subsidies to renewable energy sources, such as wind and solar energy.
The nuclear power station is expected to begin operating in 2023.