PROBLEM TO BE SOLVED: To provide a method of sterilizing a pure water production apparatus for pharmaceuticals capable of improving the hot water sterilizing efficiency and of ultimately inhibiting effects exerted onto an electric deionizer at the time of a hot water sterilizing treatment and a pure water production apparatus for pharmaceuticals.SOLUTION: In a provided method of sterilizing a pure water production apparatus, a pressure sensor 14 is configured within a permeated water pipeline of a reverse osmotic membrane device 12, and the rotation frequency of a pump P1 is controlled so as to realize a fixed output of the pressure sensor while hot water is being circulated through a treatment line L1 and circulatory lines moreover, a pure water production apparatus for pharmaceuticals furnished with a pump P1, a heat exchanger 11, a reverse osmotic membrane device 12, and an electric deionizer 13 in proper order along a treatment line L1, with circulatory lines connecting, to a raw water tank 10 via ON-OFF valves, a concentrated water pipeline for the reverse osmotic membrane device, a concentrated water pipeline and an electrolyzed water pipeline for the electric deionizer, and a treated water pipeline for the electric deionizer, with a pressure sensor 14 installed within a permeated water pipeline for the reverse osmotic membrane device, and with a controller 15 for controlling the rotation frequency of the pump based on the output of the pressure sensor is also provided.