Over the past decade, machine learning (ML) and artificial intelligence (AI) have become increasingly prevalent in the medical field. In the United States, the Food and Drug Administration (FDA) is responsible for regulating AI algorithms as "medical devices" to ensure patient safety. However, recent work has shown that the FDA approval process may be deficient. In this study, we evaluate the evidence supporting FDA-approved neuroalgorithms, the subset of machine learning algorithms with applications in the central nervous system (CNS), through a systematic review of the primary literature. Articles covering the 53 FDA-approved algorithms with applications in the CNS published in PubMed, EMBASE, Google Scholar and Scopus between database inception and January 25, 2022 were queried. Initial searches identified 1505 studies, of which 92 articles met the criteria for extraction and inclusion. Studies were identified for 26 of the 53 neuroalgorithms, of which 10 algorithms had only a single peer-reviewed publication. Performance metrics were available for 15 algorithms, external validation studies were available for 24 algorithms, and studies exploring the use of algorithms in clinical practice were available for 7 algorithms. Papers studying the clinical utility of these algorithms focused on three domains: workflow efficiency, cost savings, and clinical outcomes. Our analysis suggests that there is a meaningful gap between the FDA approval of machine learning algorithms and their clinical utilization. There appears to be room for process improvement by implementation of the following recommendations: the provision of compelling evidence that algorithms perform as intended, mandating minimum sample sizes, reporting of a predefined set of performance metrics for all algorithms and clinical application of algorithms prior to widespread use. This work will serve as a baseline for future research into the ideal regulatory framework for AI applications worldwide.