An interface in heterostructures formed by stacking two-dimensional magnets with metals could offer unprecedented electronic and magnetic properties. Here, in a heterostructure with monolayer CrI3 adsorbed on metals (Pb, Ag, Hf, and Au), we find that the nature of the CrI3-metal interface contact is spin-selective, i.e. Ohmic and Schottky contacts for the majority and minority spin channels, respectively. This spin-selective phenomenon is attributed to n-doping, and thus half metallicity of CrI3 in the heterostructure. For the Schottky contact, the slope parameter of a Schottky barrier height is found around 0.15, indicating a strong Fermi level pinning at the CrI3/metal interface. This strong Fermi level pinning is a result of two interfacial behaviors: interface gap states induced by a strong interaction between CrI3 and metals, and a interface dipole generated by charge transfer. These findings could pave the way for the free design of an electrical contact type by manipulating the spin channel in a heterostructure, and enable two-dimensionalmagnets-based versatile spintronics.