Stellar feedback, in the form of interstellar shocks, shapes the structure of the interstellar medium (ISM) and is essential for the chemistry, structure, thermodynamics, and kinematics of interstellar gas. Stellar winds, young supernova explosions, and protostellar outflows drive powerful, high-velocity shocks, while the origin of much-lower-velocity shocks (< 10 km/s) in the diffuse and translucent ISM is not understood. Direct observational evidence for interstellar shocks caused by mechanisms other than stellar winds and supernovae, as well as constraints for their importance in the diffuse ISM, have been lacking. The SiO molecule is often considered an unambiguous way to trace interstellar shocks. We present the most sensitive survey to date of SiO in absorption, obtained with the Northern Extended Millimeter Array interferometer. We detect SiO in 5/8 directions probing diffuse and translucent environments without ongoing star formation. Our results demonstrate that SiO formation in the diffuse ISM (i.e., in the absence of significant star formation and stellar feedback) is more widespread and effective than previously reported. The observed SiO linewidths are all <4 km/s, which can be formed via low-velocity shocks, i.e., not outflows, stellar winds, or supernovae. Yet, the SiO abundances we detect are typically 1 to 2 orders of magnitude higher than previously reported in quiescent environments. The detection of SiO in diffuse and translucent environments where standard, UV-dominated chemical models have failed to account for high chemical abundances suggests that non-equilibrium effects are important to diffuse interstellar chemistry and that low-velocity shocks are effective in stirring up diffuse gas and dust. Our results also emphasize the need for observational constrains on the distribution of Si in the gas phase and grain mantles, which are crucial for understanding the physics of grain processing and diffuse interstellar chemistry.