Data mining (DM) and machine learning (ML) applications in medical diagnostic systems are budding. Data privacy is essential in these systems as healthcare data are highly sensitive. The proposed work first discusses various privacy and security challenges in these systems. To address these next, we discuss different privacy-preserving (PP) computation techniques in the context of DM and ML for secure data evaluation and processing. The state-of-the-art applications of these systems in healthcare are analyzed at various stages such as data collection, data publication, data distribution, and output phases regarding PPDM and input, model, training, and output phases in the context of PPML. Furthermore, PP federated learning is also discussed. Finally, we present open challenges in these systems and future research directions.