Monolayer transition metal dichalcogenides (TMDs) and their van der Waals heterostructures have been experimentally and theoretically demonstrated as potential candidates for photovoltaic and optoelectronic devices due to the suitable bandgap and excellent light absorption. In this work, we report the observation of photodiode behavior in (both n- and p- type) silicon/monolayer MoS2 vertical heterostructures. The photocurrent and photoresponsivity of heterostructures photodiodes were dependent both on the incident light wavelength and power density, and the highest photoresponsivity of 7.2 A/W was achieved in n-Si/monolayer MoS2 vertical heterostructures photodiodes. Compared with n-Si/MoS2 heterostructures, the photoresponsivity of p-Si/MoS2 heterostructure was much lower. Kelvin probe microscope (KFM) results demonstrated the more efficient separation of photogenerated excitons in n-Si/MoS2 than that in p-Si/MoS2. Coupling KFM results with band alignments of (p-, n-) Si/MoS2 heterostructures, the origins of photodiode-like phenomena of p-Si/MoS2 and n-Si/MoS2 have been unveiled, that is intrinsic built-in electric field in p-n junction, and modulated barrier height and width at the interface in n-n junction. Our work may benefit to the deep understanding of the integration of two-dimensional materials with more conventional three-dimensional semiconductors, and then contribute to the developments in the area of van der Waals heterostructures.