Understanding complex machine learning and artificial intelligence models have always been challenging because these models are black-box, and often we don't know what information models rely upon to infer. Explainable Artificial Intelligence (XAI) has emerged as a new exciting field to explain and understand these machine learning models as humans can understand and improve them. In the past few years, there have been numerous research articles on explainable artificial intelligence for medical and healthcare. 1687 documents are being studied and analysed using bibliometric methods in this work. There are certain systematic reviews on the same topic, but this study is the first of its kind to use a quantitative method to analyze a large number of publications. The results of this study show that the research in this field took place in 2011, and there have been quite many publications in the following years. We have also identified top-cited journals and articles. Through thematic analysis, we have found some important thematic areas of research in the field of XAI for medical and healthcare. The findings showed that the USA is the global leader in XAI research, followed by China and Canada at second and third place, respectively.