Hydrogen (H2) is widely viewed as critical to the decarbonization of industry and transportation. Water electrolysis powered by renewable electricity, commonly referred to as green H2, can be used to generate H2 with low carbon dioxide emissions. Herein, we analyze the critical mineral and energy demands associated with green H2 production under three different hypothetical future demand scenarios, ranging from 100–1,000 Mtpa H2. For each scenario, we calculate the critical mineral demands required to build water electrolyzers (i.e., electrodes and electrolyte) and to build dedicated or additional renewable electricity sources (i.e., wind and solar) to power the electrolyzers. Our analysis shows that scaling electrolyzer and renewable energy technologies that use platinum group metals and rare earth elements will likely face supply constraints. Specifically, larger quantities of lanthanum, yttrium, or iridium will be needed to increase electrolyzer capacity and even more neodymium, silicon, zinc, molybdenum, aluminum, and copper will be needed to build dedicated renewable electricity sources. We find that scaling green H2 production to meet projected net-zero targets will require ∼24,000 TWh of dedicated renewable energy generation, which is roughly the total amount of solar and wind projected to be on the grid in 2050 according to some energy transition models. In summary, critical mineral constraints may hinder the scaling of green H2 to meet global net-zero emissions targets, motivating the need for the research and development of alternative, low-emission methods of generating H2.