A novel high-entropy alloy (HEA) with aluminum as the principal constituent was produced and investigated. The objective of this study was to evaluate an alloy design based on raw materials sourced from the Greek industry and to assess the effects of heat treatment on the microstructure and mechanical properties of the Al57-Zn22.3-Cu11.7-Mg9 (wt.%) alloy. The alloy design was performed using the CALPHAD approach in conjunction with Thermo-Calc software. Phase-diagram calculations successfully predicted the phase constitution of the alloy, particularly at elevated temperatures close to the solidus. Alloy casting was carried out in an induction furnace without a protective atmosphere. The selection of the melting temperature and the sequence of raw material additions were determined based on the calculated phase diagrams and the melting and boiling points of the constituent elements. Heat-treatment schedules were designed to investigate possible microstructural modifications in the alloy. Two treatment temperatures, 300 °C and 400 °C, were employed with holding times of 8 h and 24 h, followed by water quenching. Microstructural characterization and phase identification of both the as-cast and heat-treated specimens were conducted using optical microscopy and scanning electron microscopy. The Al-based alloy was found to consist of three principal phases: a primary Al-rich FCC matrix, a secondary θ phase, and a possible Fe-rich intermetallic compound, together with a eutectic microstructure. Heat treatment resulted in coarsening of the eutectic structure and promoted the formation of the Al2-Cu phase. The mechanical properties of the as-cast and heat-treated alloys were evaluated through hardness measurements at room temperature. The hardness results were consistent with the microstructural observations, indicating that heat treatment did not produce significant changes in the mechanical response of the alloy.