Two-dimensional (2D) MoSi\(_2\)N\(_4\) monolayer is a new class of air-stable 2D semiconductor possessing exceptional electrical and mechanical properties. Despite intensive research efforts devoted to unearth the material properties of MoSi\(_2\)N\(_4\) recently, the physics of electrical contacts to MoSi\(_2\)N\(_4\) remains largely unaddressed so far. Here we study the van der Waals heterostructures composed of MoSi\(_2\)N\(_4\) vertically contacted by graphene and NbS\(_2\) monolayers using first-principle density functional theory calculations. We show that MoSi\(_2\)N\(_4\)/NbS\(_2\) contact exhibits an ultralow Schottky barrier height (SBH) which is beneficial for electronic device applications. For MoSi\(_2\)N\(_4\)/graphene contact, the SBH can be modulated via interlayer distance or via external electric fields, thus opening up an opportunity for reconfigurable and tunable nanoelectronic devices. Our findings provide new insights on the physics of 2D electrical contact to MoSi\(_2\)N\(_4\), and shall pave an important first step towards the design of high efficiency electrical contacts for MoSi\(_2\)N\(_4\)-based electronic and optoelectronic devices.