Static non-reciprocity, characterized by asymmetric responses to identical static loads, has attracted significant interest for its potential to enable one-way transmission and directional control in various systems. Multistable mechanical metamaterials, engineered materials with tailored architectures capable of achieving multiple stable configurations under external stimuli, offer a promising platform for realizing tunable static non-reciprocity. Here, a class of multistable metamaterials is introduced that leverage a self-locking mechanism, integrating reentrant beams with thin beam-shaped snap-fit elements. Through the self-locking of these snap-fit elements, the metamaterial can achieve multiple, controllable, interlocked stable states. Its mechanical properties, including stiffness, strength, multistability, and deformation modes, can be precisely programmed by adjusting geometric parameters and component layouts. Furthermore, the compression-induced interlocked stable configurations, combined with geometric asymmetries, enable the metamaterial to exhibit programmable static non-reciprocity in displacement fields with nonlinear responses. The demonstrated versatility in multistability and programmable mechanical non-reciprocity paves the way for applications in energy absorption and harvesting, soft devices, and robotics.