Background Chronic neuropsychological sequelae following SARS-CoV-2 infection, including depression, anxiety, fatigue, and general cognitive difficulties, are a major public health concern. Given the potential impact of long-term neuropsychological impairment, it is important to characterize the frequency and predictors of this post-infection phenotype. Methods The Epidemiology, Immunology, and Clinical Characteristics of Emerging Infectious Diseases with Pandemic Potential (EPICC) study is a longitudinal study assessing the impact of SARS-CoV-2 infection in U.S. Military Healthcare System (MHS) beneficiaries, i.e. those eligible for care in the MHS including active duty servicemembers, dependents, and retirees. Four broad areas of neuropsychological symptoms were assessed cross-sectionally among subjects 1–6 months post-infection/enrollment, including: depression (Patient Health Questionnaire-9), anxiety (General Anxiety Disorder-7), fatigue (PROMIS® Fatigue 7a), and cognitive function (PROMIS® Cognitive Function 8a and PROMIS® Cognitive Function abilities 8a). Multivariable Poisson regression models compared participants with and without SARS-CoV-2 infection history on these measures, adjusting for sex, ethnicity, active-duty status, age, and months post-first positive or enrollment of questionnaire completion (MPFP/E); models for fatigue and cognitive function were also adjusted for depression and anxiety scores. Results The study population included 2383 participants who completed all five instruments within six MPFP/E, of whom 687 (28.8%) had at least one positive SARS-CoV-2 test. Compared to those who had never tested positive for SARS-CoV-2, the positive group was more likely to meet instrument-based criteria for depression (15.4% vs 10.3%, p<0.001), fatigue (20.1% vs 8.0%, p<0.001), impaired cognitive function (15.7% vs 8.6%, p<0.001), and impaired cognitive function abilities (24.3% vs 16.3%, p<0.001). In multivariable models, SARS-CoV-2 positive participants, assessed at an average of 2.7 months after infection, had increased risk of moderate to severe depression (RR: 1.44, 95% CI 1.12–1.84), fatigue (RR: 2.07, 95% CI 1.62–2.65), impaired cognitive function (RR: 1.64, 95% CI 1.27–2.11), and impaired cognitive function abilities (RR: 1.41, 95% CI 1.15–1.71); MPFP/E was not significant. Conclusions Participants with a history of SARS-CoV-2 infection were up to twice as likely to report cognitive impairment and fatigue as the group without prior SARS-CoV-2 infection. These findings underscore the continued importance of preventing SARS-CoV-2 infection and while time since infection/enrollment was not significant through 6 months of follow-up, this highlights the need for additional research into the long-term impacts of COVID-19 to mitigate and reverse these neuropsychological outcomes.