MLOps (Machine Learning Operations) is an engineering approach to streamline the development, deployment and maintenance of machine learning (ML) solutions in an operational environment. Managing the ML life-cycle at scale poses a variety of challenges which MLOps addresses, from the inter-dependency of various systems and their interoperability to the deployment of scalable pipelines. The maritime industry is no exception to this. This sector encounters distinct challenges in implementing machine learning operations, such as predicting the weather, optimizing shipping routes, and detecting anomalies in vessel behaviour. These requirements are addressed by creating specialized ML models tailored to the maritime domain. However, developing and deploying these models can be challenging due to the complexity of the maritime environment and the need for real-time decision-making. This study uses a systematic mapping analysis to evaluate and index existing literature on frameworks and practices for MLOps solutions that would be suitable for maritime applications. The discussion section addresses recommendations for applying MLOps to the maritime domain, difficulties with implementation and possible solutions, security, privacy, and already-implemented use cases, as well as future perspectives.