A hybrid nanocomposite comprising nanosized ZrO2 and graphene nanoplatelet (GNP)-reinforced Cu matrix was synthesised via powder metallurgy. The influence of sintering temperature and GNP content on the electrical and mechanical behaviour of the Cu–ZrO2/GNP nanocomposite was investigated. The ZrO2 concentration was fixed at 10% for all the composites. Upon increasing the GNP concentration up to 0.5%, a significant improvement was observed in the compressive strength, microhardness, and electrical conductivity of the composite. Furthermore, the properties were significantly improved by increasing the sintering temperature from 900 to 1000 ◦C. The compressive strength, hardness, and electrical conductivity of Cu–10%ZrO2/0.5%GNP were higher than those of the Cu–ZrO2 nanocomposite by 60, 21, and 23.8%, respectively. This improvement in the mechanical properties is because of the decrease in the crystallite size and dislocation spacing, which increases the dislocation density, thereby increasing the impedance towards dislocation movement. The lower stacking fault energy of the hybrid nanocomposites enables easier electron transfer within and between the Cu grains, resulting in an improved electrical conductivity. The enhancement in strength and electrical conductivity were aided by the GNPs and ZrO2 nanoparticles that were dispersed widely in the Cu matrix.