Petr Spilka, a spokesman for the Dukovany plant, says the decision poses no safety threat.
He said the problem arose Monday on one of the three pipes used for cooling the plant's technical and security systems.
He said today that authorities decided to shut down two nuclear reactors because it was not able to fix the problem in three days, a requirement of safety regulations.
The two remaining reactors at the plant have not been affected.
It is not immediately clear how much time it will take to fix the problem.