The virus was found in Block B of the nuclear reactor at Gundremmingen in western Bavaria, a statement released by the power plant said.
The malware is well known to IT specialists and it attempts to create a connection to the internet without the user of the computer choosing to do so, the statement added.
But the company insisted that the virus posed no danger to the public as all the computers which are responsible for controlling the plant are disconnected from one another and not connected to the internet.
The virus is also not capable of manipulating the functions of the power plant, the statement claims.
State authorities have been informed about the issues and specialists from the energy firm RWE are examining the computer system to asses how it became infected with the virus.
A spokesperson for the company assured Die Zeit that all of the computers which were important for the running of the power plant had been checked and none of them contained a virus.
Malware can infect computers in a multitude of ways, and is not necessarily intentionally placed there by a third party. The owner of the computer can unwittingly download it by clicking on a link in an email or by downloading a harmless looking file.
The power plant claimed that all the computers in their premises are fitted with antivirus software. But they have not said how the software did not detect the virus.
In a report published last year, the Federal Office for Security in IT (BSI) warned that attacks on industrial facilities could pose a threat to the country.
“Targeted attacks normally target office computers or engineering workstations,” the report notes.
“It has often been the case that the spread of such attacks on industrial facilities right into the production chain have not been sufficiently stopped."
That such an attack could target a nuclear facility, causing a meltdown, is unlikely, the BSI said.
Speaking to Die Welt am Sonntag on Sunday, BSI head Arne Schönbohm said that fears of a cyber attack leading to an explosion at a nuclear facility were "nonsense".
Germans are very sensitive to the dangers of nuclear technology, even as Tuesday marks 30 years since the Chernobyl disaster. As recent as 2010, officials found traces of radioactivity connected to the 1986 catastrophe in German wildlife, like wild boar.
Shortly after the Fukushima meltdown in 2011, Chancellor Angela Merkel announced that the country would phase out nuclear power by 2021.
In recent weeks doomsday nuclear scenarios have again been filling column inches in newspapers.
First, several newspapers reported that the terrorists behind the Paris attacks had the plans for a German nuclear facility, a claim later denied by German intelligence.
Then, days later, it was found that inspectors responsible for carrying out safety checks at two nuclear plants had submitted fake reports.