(1) Background: There is a need for a brief assessment of cognitive function, both in patient care and scientific research, for which the Montreal Cognitive Assessment (MoCA) is a psychometrically reliable and valid tool. However, fine-grained normative data allowing for adjustment for age, education, and/or sex are lacking, especially for its Memory Index Score (MIS). (2) Methods: A total of 820 healthy individuals aged 18–91 (366 men) completed the Dutch MoCA (version 7.1), of whom 182 also completed the cued recall and recognition memory subtests enabling calculation of the MIS. Regression-based normative data were computed for the MoCA Total Score and MIS, following the data-handling procedure of the Advanced Neuropsychological Diagnostics Infrastructure (ANDI). (3) Results: Age, education level, and sex were significant predictors of the MoCA Total Score (Conditional R2 = 0.4, Marginal R2 = 0.12, restricted maximum likelihood (REML) criterion at convergence: 3470.1) and MIS (Marginal R2 = 0.14, REML criterion at convergence: 682.8). Percentile distributions are presented that allow for age, education and sex adjustment for the MoCA Total Score and the MIS. (4) Conclusions: We present normative data covering the full adult life span that can be used for the screening for overall cognitive deficits and memory impairment, not only in older people with or people at risk of neurodegenerative disease, but also in younger individuals with acquired brain injury, neurological disease, or non-neurological medical conditions.