The approval, granted in March, removes the last major obstacle to the €12.5 billion ($13.2 billion) expansion of the Paks plant, Hungary's only nuclear facility.
"I strictly reject the expansion of the Paks nuclear plant," Austrian Chancellor Christian Kern said in a statement.
"Even the European Commission has concluded in its report that the expansion of this nuclear plant will never be profitable without massive state subsidies."
Kern did not specify when the complaint would be filed with the European Court of Justice, but said lawyers were currently checking the government's complaint.
Built with Soviet-era technology in the 1980s during Hungary's communist period, the plant outside Budapest currently provides around 40 percent of its electricity needs.
The construction of two new reactors is part of a 2014 deal struck between Hungary's right-wing Prime Minister Victor Orban and ally Russian President Vladimir Putin.
The work, to be carried out be Moscow's state-owned Rosatom, is set to more than double the plant's capacity.
EU authorities had been under pressure to take a close look at the agreement amid fears the Kremlin was using it to meddle further with the bloc's sensitive energy sector.
The European Commission gave its seal of approval after judging that the project met EU rules on state aid "on the basis of commitments made by Hungary to limit distortions of competition".
Fiercely anti-nuclear Austria had denounced the move at the time and already threatened legal action.
Kern's announcement comes two days before a snap election, which could see his Social Democrat party relegated to the opposition corner by hardline conservatives led by Sebastian Kurz, 31.