The incorporation of data analytics in the healthcare industry has made significant progress, driven by the demand for efficient and effective big data analytics solutions. Knowledge graphs (KGs) have proven utility in this arena and are rooted in a number of healthcare applications to furnish better data representation and knowledge inference. However, in conjunction with a lack of a representative KG construction taxonomy, several existing approaches in this designated domain are inadequate and inferior. This paper is the first to provide a comprehensive taxonomy and a bird's eye view of healthcare KG construction. Additionally, a thorough examination of the current state-of-the-art techniques drawn from academic works relevant to various healthcare contexts is carried out. These techniques are critically evaluated in terms of methods used for knowledge extraction, types of the knowledge base and sources, and the incorporated evaluation protocols. Finally, several research findings and existing issues in the literature are reported and discussed, opening horizons for future research in this vibrant area.