Shock and vibration hazards to civil structures are common and come not only from earthquakes but most often from mining operations or foundation work involving the installation of piles using hammer-driving and vibrating technology. The purpose of this study is to present test methods for low-cost MEMS accelerometers in terms of their selection for low-amplitude acceleration vibration-prone object-monitoring systems. Tests of 24 commercially available digital accelerometers were carried out on a custom-built test bench, selecting four models for detailed tests conducted on a specially built precision vibration table capable of inflicting accelerations at frequencies of 1–2 Hz, using displacements as small as a few micrometers. The analysis of the results was based, among other things, on a modified method of determining the signal-to-noise ratio (SNR) and also on the idea of the effective number of bits (ENOB). The results of the analysis showed that among low-cost MEMS accelerometers, there are some that are successfully suitable for the monitoring and warning of excessive vibration hazards in situations where objects are extremely sensitive to such impacts (e.g., treatment rooms in hospitals). Examples of accelerometers capable of detecting harmonic vibrations with amplitudes as small as 10 mm/s² or impulsive shocks with amplitudes of at least 70 mm/s² are indicated.