Nanoindentation experiments with a Berkovich indenter and a spherical indenter were performed to study the effects of annealing at temperatures below the glass transition temperature and room temperature ion irradiation on the near surface mechanical response of Ti40Cu32Pd14Zr10Sn2Si2 metallic glass (MG) ribbons. The specimens were isothermally annealed in vacuum at 573 K and 673 K for 4 hrs. Annealing was seen to increase the hardness of the specimens and decrease their ductility. The annealed specimens were subsequently irradiated by 3.5 MeV Cu2+ ions at room temperature using a fluence of 1 × 1012 ions/cm2 or 1 × 1016 ions/cm2. Nanoindentation experiments on the annealed and irradiated specimens showed a reduction in hardness and an increase in ductility for the specimens irradiated at a fluence of 1 × 1012 ions/cm2. Although the values of the mean contact pressure and critical shear stress under the spherical indenter showed an easier formation of shear bands after irradiation, increasing the irradiation fluence to 1 × 1016 ions/cm2 was seen to increase the hardness value and decrease the ductility of the specimens.