Smart healthcare systems are gaining popularity with the rapid development of intelligent sensors, the Internet of Things (IoT) applications and services, and wireless communications. However, at the same time, several vulnerabilities and adversarial attacks make it challenging for a safe and secure smart healthcare system from a security point of view. Machine learning has been used widely to develop suitable models to predict and mitigate attacks. Still, the attacks could trick the machine learning models and misclassify outputs generated by the model. As a result, it leads to incorrect decisions, for example, false disease detection and wrong treatment plans for patients. In this paper, we address the type of adversarial attacks and their impact on smart healthcare systems. We propose a model to examine how adversarial attacks impact machine learning classifiers. To test the model, we use a medical image dataset. Our model can classify medical images with high accuracy. We then attacked the model with a Fast Gradient Sign Method attack (FGSM) to cause the model to predict the images and misclassify them inaccurately. Using transfer learning, we train a VGG-19 model with the medical dataset and later implement the FGSM to the Convolutional Neural Network (CNN) to examine the significant impact it causes on the performance and accuracy of the machine learning model. Our results demonstrate that the adversarial attack misclassifies the images, causing the model's accuracy rate to drop from 88% to 11%.