Sarcopenia is a gradual and generalized skeletal muscle (SKM) syndrome, characterized by the impairment of muscle components and functionality. Hydrogen sulfide (H2S), endogenously formed within the body from the activity of cystathionine-γ-lyase (CSE), cystathionine- β-synthase (CBS), and mercaptopyruvate sulfurtransferase, is involved in SKM function. Here, in an in vitro model of sarcopenia based on damage induced by dexamethasone (DEX, 1 μM, 48 h treatment) in C2C12-derived myotubes, we investigated the protective potential of exogenous and endogenous sources of H2S, i.e., glucoraphanin (30 μM), L-cysteine (150 μM), and 3-mercaptopyruvate (150 μM). DEX impaired the H2S signalling in terms of a reduction in CBS and CSE expression and H2S biosynthesis. Glucoraphanin and 3-mercaptopyruvate but not L-cysteine prevented the apoptotic process induced by DEX. In parallel, the H2S-releasing molecules reduced the oxidative unbalance evoked by DEX, reducing catalase activity, O2− levels, and protein carbonylation. Glucoraphanin, 3-mercaptopyruvate, and L-cysteine avoided the changes in myotubes morphology and morphometrics after DEX treatment. In conclusion, in an in vitro model of sarcopenia, an impairment in CBS/CSE/H2S signalling occurs, whereas glucoraphanin, a natural H2S-releasing molecule, appears more effective for preventing the SKM damage. Therefore, glucoraphanin supplementation could be an innovative therapeutic approach in the management of sarcopenia.