Background: Natural Language Processing (NLP) and Large Language Models (LLMs) hold largely untapped potential in infectious disease management. This review explores their current use and uncovers areas needing more attention. Methods: This analysis followed systematic review procedures, registered with PROSPERO. We conducted a search across major databases including PubMed, Embase, Web of Science, and Scopus, up to December 2023, using keywords related to NLP, LLM, and infectious diseases. We also employed the QUADAS-2 tool for evaluating the quality and robustness of the included studies. Results: Our review identified 15 studies with diverse applications of NLP in infectious disease management. Notable examples include GPT-4's application in detecting urinary tract infections and BERTweet's use in Lyme Disease surveillance through social media analysis. These models demonstrated effective disease monitoring and public health tracking capabilities. However, the effectiveness varied across studies. For instance, while some NLP tools showed high accuracy in pneumonia detection and high sensitivity in identifying invasive mold diseases from medical reports, others fell short in areas like bloodstream infection management. Conclusion: This review highlights the yet-to-be-fully-realized promise of NLP and LLMs in infectious disease management. It calls for more exploration to fully harness AI's capabilities, particularly in the areas of diagnosis, surveillance, predicting disease courses, and tracking epidemiological trends.