Metal-oxide/silicon carrier-selective heterojunctions 5 be a low-cost high-efficiency alternative to conventional silicon solar cells. Here, a passivated Si/cuprous oxide (Cu$_2$O) hole-selective heterojunction with high open-circuit voltage (VOC) is reported. Cu$_2$O is abundant, nontoxic, and can be deposited at low temperatures and potentially at low cost. The Si/Cu$_2$O heterojunction has a large conduction band offset of 0.9 eV and a negligible valence band offset, which blocks the transport of electrons but allows the transport of holes. The as-deposited hetero-interface is limited due to a high density of defects. However, the interface defect density can be reduced by a 1.2 nm thin tunneling SiO2 layer, which enables the realization of a Si/Cu$_2$O heterojunction solar cell with an open-circuit voltage (VOC) of 0.528 V, a 200 mV improvement over the state-of-the-art.