Her order came as the hackers posted more data online on Tuesday, the Yonhap news agency reported.
Officials said earlier that only designs and manuals of plant equipment were leaked, and reactors' innermost networks were not compromised.
South Korea has not ruled out North Korean involvement in the attack.
Ms Park made no mention of any link between the North and the cyber attack but said the plants remained safe.
She told officials in a cabinet meeting to check their preparations and inspect safeguards against cyber terrorism on the nation's key facilities, including nuclear reactors.
She called the data leak a "grave situation that is unacceptable", and said there should have been "not a trace of lapse as a matter of national security", in remarks reported by Reuters.
Yonhap reported that the hacker posted on Twitter on Tuesday afternoon four files of reactor-related information, including what appeared to be diagrams of facilities, and reasserted demands that reactors be suspended.
A file picture dated 22 March 2013 shows four reactors of the nuclear power plant in Wolseong, South Korea.
Korea Hydro and Nuclear Power Co Ltd (KHNP) has been conducting large-scale drills at four nuclear power plant complexes.
A hacker calling himself "president of the anti-nuclear reactor group" had posted blueprints of nuclear reactors on social media on Friday, in the latest in a series of postings since 15 December, and demanding some reactors be closed by Christmas.
Officials have asked the US Federal Bureau of Investigation for help in finding the hacker, after discovering that IP addresses in multiple locations had been used, including South Korea, the US and Japan, reported The Korea Times.
North Korea outage
Ms Park in the same cabinet meeting also referred to the recent hacking of US movie studio Sony Pictures, saying it was a reminder of the "seriousness of cyber terrorism".
The US has attributed the Sony hacking to North Korea over the film The Interview, and President Barack Obama has vowed the US would take a "proportionate response". Pyongyang has denied its involvement.
North Korea saw its internet go down from Monday night to Tuesday morning. The cause for the outage is not yet known.
