Synthetic materials and heterostructures obtained by the controlled stacking of exfoliated monolayers are emerging as attractive functional materials owing to their highly tunable properties. We present a detailed scanning tunneling microscopy and spectroscopy study of single layer MoS₂-on-gold heterostructures as a function of the twist angle. We find that their electronic properties are determined by the hybridization of the constituent layers and are modulated at the moiré period. The hybridization depends on the layer alignment, and the modulation amplitude vanishes with increasing twist angle. We explain our observations in terms of a hybridization between the nearest sulfur and gold atoms, which becomes spatially more homogeneous and weaker as the moiré periodicity decreases with increasing twist angle, unveiling the possibility of tunable hybridization of electronic states via twist angle engineering.