The demand for real-time, affordable, and efficient smart healthcare services is increasing exponentially due to the technological revolution and burst of population. To meet the increasing demands on this critical infrastructure, there is a need for intelligent methods to cope with the existing obstacles in this area. In this regard, edge computing technology can reduce latency and energy consumption by moving processes closer to the data sources in comparison to the traditional centralized cloud and IoT-based healthcare systems. In addition, by bringing automated insights into the smart healthcare systems, artificial intelligence (AI) provides the possibility of detecting and predicting high-risk diseases in advance, decreasing medical costs for patients, and offering efficient treatments. The objective of this article is to highlight the benefits of the adoption of edge intelligent technology, along with AI in smart healthcare systems. Moreover, a novel smart healthcare model is proposed to boost the utilization of AI and edge technology in smart healthcare systems. Additionally, the paper discusses issues and research directions arising when integrating these different technologies together.