Background: Embodied artificial intelligence (EAI), integrating advanced AI algorithms with robotic platforms capable of sensing, planning, and acting, has emerged as a transformative approach in healthcare delivery. This systematic review synthesizes evidence on robotic perception, decision-making, and clinical impact of EAI systems in healthcare settings. Methods: Following PRISMA 2020 guidelines, we searched PubMed/MEDLINE, Scopus, Web of Science, IEEE Xplore, and ACM Digital Library for studies published between January 2020 and August 2025. Seventeen studies met eligibility criteria, spanning four domains: surgical assistance, rehabilitation, hospital logistics, and telepresence. The protocol was prospectively registered in PROSPERO under ID: CRD420261285936. Results: Perception architectures predominantly employed multimodal sensor fusion, combining vision with force/torque, depth, and physiological signals. Decision-making approaches included imitation learning, reinforcement learning, and hybrid symbolic-neural control. Key findings indicate that surgical robots demonstrated consistency advantages in specific experimental tasks, rehabilitation robotics produced statistically significant improvements (SMD = 0.29) across 396 randomized controlled trials, and both logistics and telepresence systems achieved very high operational success levels. Nonetheless, important barriers remain, including limited external validation, small sample sizes, and insufficient cost-effectiveness data. Conclusions: Future research should prioritize standardized benchmarks, prospective multicenter trials, and patient-centered outcome measures to facilitate clinical translation of EAI technologies.