We investigated the etching behavior of silicon oxide (SiOx) and silicon nitride (SiNx) in narrow-gap, high-pressure (3.3 kPa) hydrogen (H2) plasma under various etching conditions. Maximum etching rates of 940 and 240 nm/min for SiOx and SiNx, respectively, were obtained by optimizing the H2 gas flow rate. The dependence of the etching rate on gas flow rate implied that effective elimination of etching products is important for achieving high etching rates because it prevents redeposition. The sample surfaces, especially the oxide surfaces, were roughened and contained numerous asperities after etching. Etching rates of both SiOx and SiNx decreased as the temperature was raised. This suggests that atomic H adsorption, rather than H-ion bombardment, is an important step in the etching process. X-ray photoelectron spectroscopy revealed that the etched nitride surface was enriched in silicon (Si), suggesting that the rate-limiting process in high-pressure H2 plasma etching is Si etching rather than nitrogen abstraction. The etching rate of SiOx was three times higher than that of SiNx despite the higher stability of Si–O bonds than Si–N ones. One reason for the etching difference may be the difference between the bond densities of SiOx and SiNx. This study presents a relatively non-toxic, low-cost, and eco-friendly dry etching process for Si-based dielectrics using only H2 gas in comparison with the conventional F-based plasma etching methods.