Channel electron multiplier (CEM) and microchannel plate (MCP) detectors are routinely used in space instrumentation for measurement of space plasmas. Our goal is to understand the relative sensitivities of these detectors to penetrating radiation in space, which can generate background counts and shorten detector lifetime. We use 662 keV γ-rays as a proxy for penetrating radiation such as γ-rays, cosmic rays, and high-energy electrons and protons that are ubiquitous in the space environment. We find that MCP detectors are ~ 20 times more sensitive to 662 keV γ-rays than CEM detectors. This is attributed to the larger total area of multiplication channels in an MCP detector that is sensitive to electronic excitation and ionization resulting from the interaction of penetrating radiation with the detector material. In contrast to the CEM detector, whose quantum efficiency εγ for 662 keV γ-rays is found to be 0.00175 and largely independent of detector bias, the quantum efficiency of the MCP detector is strongly dependent on the detector bias, with a power law index of 5.5. Background counts in MCP detectors from penetrating radiation can be reduced using MCP geometries with higher pitch and smaller channel diameter.