Disclosed are a powder of a silver-based inorganic antimicrobial agent with superior dispersability or water permeability, composed of silver-supporting hexagonal zirconium phosphate, and an antimicrobial product and a water processing material using the silver-based inorganic antimicrobial agent powder. The silver-based inorganic antimicrobial agent containing hexagonal zirconium phosphate crystals, which has a particle size distribution to enable easy handling as a powder and contribute to exhibition of antimicrobial properties, can be prepared by a preparation method including wet-heating zirconium carbonate. When the silver-based inorganic antimicrobial agent wherein particles with a size of 10 μm to 100 μm are 90% or more on a volume basis is kneaded into resin products, since aggregation or the like may not occur and the silver-based inorganic antimicrobial agent can be easily exposed on the surface of molded articles, antimicrobial effects are thus readily exhibited on the surface.