The Martian subsurface is more favorable for organic preservation than its surface because of the shielding effect of rocks from cosmic rays and UV radiation with increasing depth. Nevertheless, the natural radioactivity on Mars owing to U, Th, and K must be considered to study the possible extant and/or extinct life. Here, we demonstrate the importance of natural radiation on the amino acid glycine in two different chemical environments, GlyFeSO4 5H2O and GlyMgSO4 5H2O, which are coordination compounds considered relevant to Mars. The results show that after a 600 kGy dose of gamma radiation, glycine was more stable when it bonded to Mg in the GlyMgSO4 5H2O coordination compound, it was less stable when it bonded to Fe in the GlyFeSO4 5H2O compound. Studies on the effects of gamma radiation on preservation of organic molecules bound to minerals and other potential compounds on Mars are significantly important in the search for biosignatures.