This paper focuses on high-entropy spinels, which represent a rapidly growing group of materials with physicochemical properties that make them suitable for hydrogen energy applications. The influence of high-pressure pure hydrogen on the chemical stability of three high-entropy oxide (HEO) sinter samples with a spinel structure was investigated. Multicomponent HEO samples were obtained via mechanochemical synthesis (MS) combined with high-temperature thermal treatment. Performing the free sintering procedure on powders after MS at 1000 °C for 3 h in air enabled achieving single-phase (Cr_0.2Fe_0.2Mg_0.2Mn_0.2Ni_0.2)₃O₄ and (Cu_0.2Fe_0.2Mg_0.2Ni_0.2Ti_0.2)₃O₄ powders with a spinel structure, and in the case of (Cu_0.2Fe_0.2Mg_0.2Ti_0.2Zn_0.2)₃O₄, a spinel phase in the amount of 95 wt.% was achieved. A decrease in spinel phase crystallite size and an increase in lattice strains were established in the synthesized spinel powders. The hydrogenation of the synthesized samples in a high-pressure hydrogen atmosphere was investigated using Sievert’s technique. The results of XRD, SEM, and EDS investigations clearly showed that pure hydrogen at temperatures of up to 250 °C and a pressure of up to 40 bar did not significantly impact the structure and microstructure of the (Cr_0.2Fe_0.2Mg_0.2Mn_0.2Ni_0.2)₃O₄ ceramic, which demonstrates its potential for application in hydrogen technologies.