The increasing availability of healthcare data requires accurate analysis of disease diagnosis, progression, and realtime monitoring to provide improved treatments to the patients. In this context, Machine Learning (ML) models are used to extract valuable features and insights from high-dimensional and heterogeneous healthcare data to detect different diseases and patient activities in a Smart Healthcare System (SHS). However, recent researches show that ML models used in different application domains are vulnerable to adversarial attacks. In this paper, we introduce a new type of adversarial attacks to exploit the ML classifiers used in a SHS. We consider an adversary who has partial knowledge of data distribution, SHS model, and ML algorithm to perform both targeted and untargeted attacks. Employing these adversarial capabilities, we manipulate medical device readings to alter patient status (disease-affected, normal condition, activities, etc.) in the outcome of the SHS. Our attack utilizes five different adversarial ML algorithms (HopSkipJump, Fast Gradient Method, Crafting Decision Tree, Carlini & Wagner, Zeroth Order Optimization) to perform different malicious activities (e.g., data poisoning, misclassify outputs, etc.) on a SHS. Moreover, based on the training and testing phase capabilities of an adversary, we perform white box and black box attacks on a SHS. We evaluate the performance of our work in different SHS settings and medical devices. Our extensive evaluation shows that our proposed adversarial attack can significantly degrade the performance of a ML-based SHS in detecting diseases and normal activities of the patients correctly, which eventually leads to erroneous treatment.