This study unveils the In-Context Evolutionary Search (ICE-SEARCH) method, the first work that melds language models (LMs) with evolutionary algorithms for feature selection (FS) tasks and demonstrates its effectiveness in Medical Predictive Analytics (MPA) applications. ICE-SEARCH harnesses the crossover and mutation capabilities inherent in LMs within an evolutionary framework, significantly improving FS through the model's comprehensive world knowledge and its adaptability to a variety of roles. Our evaluation of this methodology spans three crucial MPA tasks: stroke, cardiovascular disease, and diabetes, where ICE-SEARCH outperforms traditional FS methods in pinpointing essential features for medical applications. ICE-SEARCH achieves State-of-the-Art (SOTA) performance in stroke prediction and diabetes prediction; the Decision-Randomized ICE-SEARCH ranks as SOTA in cardiovascular disease prediction. Our results not only demonstrate the efficacy of ICE-SEARCH in medical FS but also underscore the versatility, efficiency, and scalability of integrating LMs in FS tasks. The study emphasizes the critical role of incorporating domain-specific insights, illustrating ICE-SEARCH's robustness, generalizability, and swift convergence. This opens avenues for further research into comprehensive and intricate FS landscapes, marking a significant stride in the application of artificial intelligence in medical predictive analytics.