We report on the first single-junction GaSb solar cell epitaxially grown on a Si substrate. A control stand-alone GaSb solar cell was primarily fabricated, which demonstrated a 5.90% efficiency (AM1.5G). The preparation, growth and manufacturing procedures were then adapted to create the GaSb-on-Si solar cell. The hybrid device resulted in a degraded efficiency for which comparison between experimental and simulated data revealed dominant non-radiative recombination processes. Material and electrical characterization also highlighted the impact of anti-phase domains and boundaries and threading dislocation density on the shunt resistance of the cell. Nevertheless, the GaSb-on-Si cell performance is close to recent results on the integration of GaSb solar cells on GaAs, despite a much larger lattice mismatch (12% vs 8%). Routes for improvement, concerning the material quality and cell structure, are proposed. This work lays the foundations of a GaSb-based multi-junction solar cell monolithically integrated on Si.