COVID-19 vaccination is a life-saving intervention. However, it does not come up without a risk of rare adverse events, which frequency varies between vaccines developed using different technological platforms. The increased risk of Guillain-Barré syndrome (GBS) has been reported for selected adenoviral vector vaccines but not for other vaccine types, including more widely used mRNA preparations. Therefore, it is unlikely that GBS results from the cross-reactivity of antibodies against the SARS-CoV-2 spike protein generated after the COVID-19 vaccination. This paper outlines two hypotheses according to which increased risk of GBS following adenoviral vaccination is due to (1) generation of anti-vector antibodies that may cross-react with proteins involved in biological processes related to myelin and axons, or (2) neuroinvasion of selected adenovirus vectors to the peripheral nervous system, infection of neurons and subsequent inflammation and neuropathies. The rationale behind these hypotheses is outlined, advocating further epidemiological and experimental research to verify them. This is particularly important given the ongoing interest in using adenoviruses in developing vaccines against various infectious diseases and cancer immunotherapeutics.