Deploying applications in containers has several advantages, such as rapid development, portability across different machines, and simplified maintenance. In a cloud computing environment, container scheduling algorithms coordinate with different aspects of physical systems, such as memory allocation for tasks of different users. The scheduled containers on a host may process sensitive data. For instance, containers may process healthcare information. In that case, diverse cloud environments with different components and subsystems may lead to a potential personal health information leakage and violation of data privacy. In this paper, we introduce a novel compliance-aware analysis model for provisioning containers in the cloud, that provides a HIPAA compliance model. The proposed method dynamically analyzes different requirements of HIPAA complaint containers (HIPAA parameters) and their associated risk values. Based on the risk optimization of the compliance parameters for data security and data privacy of the containers, our proposed method determines scheduling of containers that offer the lowest risk to healthcare data and to the compliance posture of the container. The model describes the resources that are associated with highlevel risks and provides real-time resource recommendation for a container scheduler to decrease the risk of HIPAA compliance violation.