In this study, ultrasonic measurements were performed on a single crystal of cubic PrNi₂Cd₂₀, down to a temperature of 0.02 K, to investigate the crystalline electric field ground state and search for possible phase transitions at low temperatures. The elastic constant (C₁₁−C₁₂)/2, which is related to the Γ₃-symmetry quadrupolar response, exhibits the Curie-type softening at temperatures below ∼30 K, which indicates that the present system has a Γ₃ non-Kramers doublet ground state. A leveling-off of the elastic response appears below ∼0.1 K toward the lowest temperatures, which implies the presence of level splitting owing to a long-range order in a finite-volume fraction associated with Γ₃-symmetry multipoles. A magnetic field–temperature phase diagram of the present compound is constructed up to 28 T for H || [110]. A clear acoustic de Haas–van Alphen signal and a possible magnetic-field-induced phase transition at H ∼26 T are also detected by high-magnetic-field measurements.