It is unknown whether neurological symptoms are associated with brain injury after SARS-CoV-2 infections and whether brain injury and related symptoms also emerge in Long-COVID patients. Biomarkers such as serum neurofilament light chain (sNfL) and glial fibrillary acidic protein (sGFAP) can be used to elucidate neuro-axonal and astroglial injuries. We investigated whether these biomarkers are associated with COVID-19 infection status, associated symptoms and Long-COVID. From 146 individuals of the general population with a post-acute, mild-to-moderate SARS-CoV-2 infection, sNfL and sGFAP were measured before, during and after (five and ten months) the infection. Individual symptoms and Long-COVID status were assessed using questionnaires. Neurological associated symptoms were described for individuals after a mild and moderate COVID-19 infection; however, sNfL (p = 0.74) and sGFAP (p = 0.24) did not change and were not associated with headache (p = 0.51), fatigue (p = 0.93), anosmia (p = 0.77) or ageusia (p = 0.47). In Long-COVID patients, sGFAP (p = 0.038), but not sNfL (p = 0.58), significantly increased but was not associated with neurological associated symptoms. Long-COVID status, but not post-acute SARS-CoV-2 infections, may be associated with astroglial injury/activation, even if neurological associated symptoms were not correlated.