It is well established that cells, tissues, and organisms exposed to low doses of ionizing radiation can induce effects in non-irradiated neighbors (non-targeted effects or NTE), but the mechanisms remain unclear. This is especially true of the initial steps leading to the release of signaling molecules contained in exosomes. Voltage-gated ion channels, photon emissions, and calcium fluxes are all involved but the precise sequence of events is not yet known. We identified what may be a quantum entanglement type of effect and this prompted us to consider whether aspects of quantum biology such as tunneling and entanglement may underlie the initial events leading to NTE. We review the field where it may be relevant to ionizing radiation processes. These include NTE, low-dose hyper-radiosensitivity, hormesis, and the adaptive response. Finally, we present a possible quantum biological-based model for NTE.