Background and Objectives: The neurocognitive sequelae of COVID-19 have attracted attention as part of post-COVID condition (PCC), yet standardized tools for screening and quantifying PCC-related cognitive impairment remain scarce. The present study aimed to develop and validate the Screening for Neurocognitive Abilities Post-COVID (SNAP-COVID), a self-report questionnaire designed to capture current symptom burden and perceived changes in cognitive functioning relative to pre-COVID status in a Greek-speaking sample. Materials and Methods: Data collection occurred in three phases between August 2024 and February 2025. Dataset A (N = 27) was used for test–retest reliability. Dataset B (N = 300) was used for exploratory factor analysis (EFA), reliability testing, and convergent validity analyses with the Brain Fog Scale (BFS). Dataset C (N = 317) was used for independent validation through confirmatory factor analysis (CFA). Results: Initial EFA of the 30-item SNAP-COVID scale suggested a four-factor model, yet further item refinement yielded a robust three-factor, 24-item solution: (1) General Cognitive Functions (17 items, α = 0.948), (2) Sensory Hypersensitivity (4 items, α = 0.829), and (3) Language and Communication (3 items, α = 0.950). The total scale demonstrated excellent internal consistency (α = 0.95). Convergent validity was evident by significant correlations between SNAP impact scores and BFS scores (r = −0.442, p < 0.001). CFA confirmed the three-factor structure with acceptable fit indices (χ²(249) = 677.29, p < 0.001; CFI = 0.882; TLI = 0.869; RMSEA = 0.074; SRMR = 0.032). Conclusions: The SNAP-COVID scale is a reliable and valid instrument. Its multidimensional structure captures global and domain-specific difficulties, addressing a critical gap in post-infectious cognitive assessment.