Impaired cognitive ability is one of the most frequently reported neuropsychiatric symptoms in the post-COVID phase among patients. It is unclear whether this condition is related to structural or functional brain changes. In this study, we present a multimodal magnetic resonance imaging study of 36 post-COVID patients and 36 individually matched controls who had a mild form of severe acute respiratory syndrome coronavirus 2 (SARS CoV-2) infection from March 2020 to February 2022. This study aimed to investigate structural and functional brain alterations and their correlation with post-COVID symptoms and neurocognitive functions. The study protocol comprised an assessment of physical fatigue [Fatigue Severity Scale (FSS)], mental fatigue (Mental Fatigue Scale (MFS)], depression [Montgomery Asberg Depression Rating Scale (MADRS)], anxiety [Hospital Anxiety and Depression Scale (HAD)], post-COVID Symptoms Severity Score, and neurocognitive status [Repeatable Battery for the Assessment of Neuropsychological Status Update (RBANS)]. The magnetic resonance imaging protocol included morphological sequences, arterial spin labeling (ASL) and dynamic susceptibility contrast-enhanced (DSC) perfusion, diffusion tensor imaging (DTI), and resting-state functional magnetic resonance imaging (fMRI) sequences. Using these protocols, the assessments of macrostructural abnormalities, perfusion, gray matter density, white matter integrity, and brain connectivity were performed. Post-COVID patients had higher levels of physical fatigue, mental fatigue, depression, and anxiety than controls and showed cognitive impairment in all the RBANS domains except in Visuospatial/Construction. The subjective mental fatigue correlated with objective impaired cognitive ability in the RBANS test, particularly in the Attention domain. There were no differences between patients and controls regarding macrostructural abnormalities, regional volumes, regional perfusion metrics, gray matter density, or DTI parameters. We observed a significant positive correlation between RBANS Total Scale Index score and gray matter volume in the right superior/middle-temporal gyrus (p < 0.05) and a significant negative correlation between the white matter integrity and post-COVID symptoms (p < 0.05) in the same area. The connectivity differences were observed between patients and controls in a few regions, including the right middle frontal gyrus, an important area of convergence of the dorsal and ventral attention networks. We also noted a positive correlation between post-COVID symptoms and increased connectivity in the right temporoparietal junction, which is part of the ventral attention system. In non-hospitalized subjects with post-COVID, we did not find any structural brain changes or changes in perfusion, compared to controls. However, we noted differences in connectivity within an important area for attention processes, which may be associated with post-COVID brain fog.