Post-COVID-19 condition can include persistent cognitive symptoms, commonly described as impaired attention, memory difficulties, slowed processing, and “brain fog.” Clinical and translational evidence implicates systemic inflammation, neurovascular dysfunction, blood–brain barrier disruption, glial inflammatory responses, oxidative stress, and altered synaptic or network function; their relative contributions remain uncertain and may differ across patient subgroups. Resveratrol is a polyphenolic compound that modifies inflammatory, redox, metabolic, endothelial, and antiviral pathways in experimental systems. This focused narrative review examines whether those actions provide a mechanistic basis for the use of resveratrol in post-COVID-19 cognitive dysfunction. Evidence was considered according to biological proximity to the intended indication, distinguishing human post-acute sequelae of SARS-CoV-2 infection (PASC) studies from acute-COVID-19, non-COVID-19 clinical, animal, organoid, and cell-based evidence. The review identifies candidate neurovascular, immune, and metabolic processes, evaluates where resveratrol evidence intersects with those processes, and distinguishes molecular observations from clinical questions that remain to be tested for to define the therapeutic potential of using resveratrol to treat post-COVID-19 cognitive impairment.