Elastic properties of cubic PrMg3 with a non-Kramers Gamma(3) doublet ground state have been investigated with ultrasonic measurements. The temperature dependence of the elastic constant (C-11-C-12)/2 in PrMg3 exhibits a characteristic minimum around 28 K and successively shows pronounced softening below 8 K down to 20 mK. The observation is well described by multipole susceptibility considering both an electric quadrupole O-v and electric hexadecapole H-v with Gamma(3g) representation for the crystal field level Gamma(3) ground state and Gamma(4) triplet excited state located at 54 K for PrMg3. The contribution of the hexadecapole in the Gamma(3)-Gamma(4) system to the multipole susceptibility should be emphasized to explain a common feature of the minimum typically observed in (C-11-C-12)/2 of Pr-based compounds PrPb3, PrAg2In, and the present PrMg3, as revealed by systematic ultrasonic measurements.