Selective removal of hydrogen sulfide (H2S) from sour natural gas mixtures is one of the key challenges facing the natural gas industry. Adsorption and pervaporation processes utilizing nanoporous materials, such as zeolites, can be alternatives to highly energy-intensive amine-based absorption processes. In this work, the adsorption behavior of binary mixtures containing H2S and methane (CH4) in seven different all-silica zeolite frameworks (CHA, DDR, PER, IFR, MFI, MOR, and MWW) is investigated using Gibbs ensemble Monte Carlo simulations at two temperatures (298 and 343 K) and pressures ranging from 1 to 50 bar. The simulations demonstrate high selectivities that, with the exception of MOR, increase with increasing H2S concentration due to favorable sorbate-sorbate interactions. The simulations indicate significant inaccuracies of predictions using unary adsorption data and ideal adsorbed solution theory. In addition, the adsorption of binary H2S/H2O mixtures in MFI is considered to probe whether the presence of H2S induces coadsorption and reduces the hydrophobic character of all-silica zeolites. The simulations show preferential adsorption of H2S from moist gases with a selectivity of about 18 over H2O.