The emergence and rapid development of the Internet of Medical Things (IoMT), an application of the Internet of Things into the medical and healthcare systems, have brought many changes and challenges to modern medical and healthcare systems. Particularly, machine learning technology can be used to process the data involved in IoMT for medical analysis and disease diagnosis. However, in this process, the disclosure of personal privacy information must receive considerable attentions especially for sensitive medical data. Cluster analysis is an important technique for medical analysis and disease diagnosis. To enable privacy-preserving cluster analysis in IoMT, this paper proposed an Efficient Differentially Private Data Clustering scheme (EDPDCS) based on MapReduce framework. In EDPDCS, we optimize the allocation of privacy budgets and the selection of initial centroids to improve the accuracy of differentially private K-means clustering algorithm. Specifically, the number of iterations of the K-means algorithm is set to a fixed value according to the total privacy budget and the minimal privacy budget of each iteration. In addition, an improved initial centroids selection method is proposed to increase the accuracy and efficiency of the clustering algorithm. Finally, we prove that the proposed EDPDCS can improve the accuracy of the differentially private k-means algorithm by comparing the Normalized Intra-Cluster Variance (NICV) produced by our algorithm on two datasets with two other algorithms.