Electronic transport through a metal|semiconductor (M|S) heterojunction is largely determined by its Schottky barrier. In 3D M|S junctions, the barrier height determines the turn-on voltage and is often pinned by the interface states, causing Fermi level pinning (FLP). The pinning strength in 3D depends on the ratio Ci/CM between the interface quantum capacitance Ci and the metal surface capacitance CM. In 2D, the interface dipole does not influence the band alignment, but still affects the Schottky barrier and transport. In light of the general interest in building 2D electronics, in this work we discover the relevant material parameters which dictate the behavior and strength of FLP in 2D M|S contacts. Using a multiscale model combining first-principles, continuum electrostatics, and transport calculations, we study a realistic Gr|MoS2 interface as an example with high interface state density (Ci/CM ≫ 1). Transport calculations show partial pinning with a strength P ∼ 0.6, while a 3D junction with similar heterogeneity gives full pinning with P = 1 as expected. We further show that in 2D M|S contacts the turn-on voltage and pinning strength are affected by a physical parameter l/λD, the ratio between the interface width l, and the thermal de Broglie wavelength λD. Pinning is absent for ideal line-contacts (l/λD = 0), but increases for realistic l/λD values.