The influence of heat treatment cycles on the phase transformation and mechanical properties of a non-equiatomic cast CrMnFeNiCu high-entropy alloy (HEA) was investigated. In its initial as-cast state, the alloy exhibited a hierarchical structure comprising dual-FCC+BCC phases. Through heat treatment at 900–950 °C, a significant amount of σ-phase formed at the expense of the Cr-Fe-rich BCC phase, resulting in a dual-FCC+BCC+ σ microstructure. However, at 1000 °C, the σ-phase underwent extensive reversion, leading to the dissolution of the hierarchical structure. The as-cast HEA, with its hierarchically structured microstructure, exhibited superior mechanical properties and lower strain-rate sensitivity than the solid solution CrMnFeCoNi (Cantor alloy) due to the strengthening by the microscale phase separation as athermal obstacles instead of the nanoscale thermal obstacles such as short-range heterogeneities in CrMnFeCoNi alloy. The thermally activated transformation of the σ-phase influenced the mechanical characteristics of the annealed HEA samples.