Herein, we carried out first-principles calculations based on density functional theory to investigate the effects of surface functionalization with hydrogen atoms on structural, dynamical and electronic properties of Cu₂Si monolayer. Pristine Cu₂Si, a metallic monolayer, has a planar hexacoordinate structure. Calculations revealed that the most favorable position of a single H atom on the Cu₂Si monolayer is at the top of a Si site. Derivatives of Cu₂Si monolayer with various H concentrations were investigated, and by performing phonon calculations, it was found that there are three stable hydrogenated structures. Specific heat of these monolayers was found to increase with the hydrogen concentration at temperatures higher than 100 K. Electronically, the hydrogenated derivatives of Cu₂Si monolayer preserve the metallic character.