In this age of Internet of Things (IoT), remote health monitoring and out-of-hospital treatment is not a distant dream. Wearable medical sensors and smartphones in the current IoT-driven environment allow for real-time monitoring of important health markers, with data quickly sent to distant specialists for analysis. Moreover, due to the onset of technological advancements like Electronic Health Records (EHR), IoT-enabled devices, Public Open health Data (POD), Linked Opened Data (LOD), remote health monitoring, vast quantities of information created in this domain as big data in health care. Intelligent storage and analysis of this big data may lead to generate critical insights for future predictions. The storage challenge of big data can be mitigated by the use of cloud computing. However, processing of Personal Health Information (PHI) on remote medical servers or cloud raises serious concern about the security of critical PHI. One immediate solution is for the information proprietors to transmit and store their delicate information in encrypted form. However, traditional encryption schemes do not support processing on that encrypted form of data. To take full advantage of cloud computing and out-of-hospital treatment, there should be a solution to process on that encrypted form of data directly. In this paper, we propose a framework which supports secure data transmission from medical sensors to distant cloud server or remote medical organizations, secure processing on that data to provide distant medical treatments and perform secure machine learning-based analytics on such sensor-generated datasets. For this secure processing, we use Fully Homomorphic Encryption(FHE) scheme, which supports direct processing on encrypted data. Our implementation shows the proposed secure framework is capable of disease detection remotely in an encrypted domain confirming PHI data confidentiality. The framework also supports performing encrypted machine learning algorithm on cloud-based medical dataset in a secure way. However, the main challenge in this case is the performance bottleneck. Parallel implementation, supported by appropriate operators, significantly improves performance, and near-practical performance is achieved conforming data security in smart health care.