The integration of Large Language Models (LLMs) into healthcare applications offers promising advancements in medical diagnostics, treatment recommendations, and patient care. However, the susceptibility of LLMs to adversarial attacks poses a significant threat, potentially leading to harmful outcomes in delicate medical contexts. This study investigates the vulnerability of LLMs to two types of adversarial attacks in three medical tasks. Utilizing real-world patient data, we demonstrate that both open-source and proprietary LLMs are susceptible to manipulation across multiple tasks. This research further reveals that domain-specific tasks demand more adversarial data in model fine-tuning than general domain tasks for effective attack execution, especially for more capable models. We discover that while integrating adversarial data does not markedly degrade overall model performance on medical benchmarks, it does lead to noticeable shifts in fine-tuned model weights, suggesting a potential pathway for detecting and countering model attacks. This research highlights the urgent need for robust security measures and the development of defensive mechanisms to safeguard LLMs in medical applications, to ensure their safe and effective deployment in healthcare settings.