Farms face various risks such as uncertainties in the natural growth process, obtaining adequate financing, volatile input and output prices, unpredictable changes in farm-related policy and regulations, and farmers‘ personal health problems. Accordingly, farmers have to make decisions to be prepared for such situations under risk or mitigate their impacts to maintain essential functions. Increasingly, a data-driven perspective is warranted where machine learning (ML) has become an essential tool for automatic extraction of useful information to support decision-making in farm management as well as risk management. ML's role in farm risk management (FRM) has recently increased with advances in technology and digitalization. This paper provides a literature review in the form of a systematic mapping study to identify the publications, trends, active research communities, and detailed reviews on the use of ML methods for FRM. Accordingly, nine research/mapping questions are designed to extract the required information. In total, we retrieved 1819 papers, of which 746 papers were selected based on the defined exclusion criteria for a detailed review. We categorized the studies based on the addressed risk types (e.g., production risk), assessments that addressed risk components (e.g., resilience), used ML types (e.g., supervised learning) and algorithms ranging from regression modeling to deep learning, addressed ML tasks (e.g., classification), data types (e.g., images), and farm types (e.g., crop-based farm). The results reveal that there is a significant increase in employing ML methods including deep learning and convolutional neural networks for FRM in recent years. The production risk and impact/damage assessment are the most frequently addressed risk type and assessment that addressed risk components in ML-FRM, respectively. In addition, research gaps and open problems are identified and accordingly insights and recommendations from risk management and machine learning perspectives are provided for future studies including the need for ML methods for different risk types (e.g., financial risk), assessments addressing different risk components (e.g., resilience assessment), and developing more advanced ML methods (e.g., reinforcement learning) for FRM.