Although cyberattacks on machine learning (ML) production systems can be destructive, many industry practitioners are ill equipped, lacking tactical and strategic tools that would allow them to analyze, detect, protect against, and respond to cyberattacks targeting their ML-based systems. In this paper, we take a significant step toward securing ML production systems by integrating these systems and their vulnerabilities into cybersecurity risk assessment frameworks. Specifically, we performed a comprehensive threat analysis of ML production systems and developed an extension to the MulVAL attack graph generation and analysis framework to incorporate cyberattacks on ML production systems. Using the proposed extension, security practitioners can apply attack graph analysis methods in environments that include ML components, thus providing security experts with a practical tool for evaluating the impact and quantifying the risk of a cyberattack targeting an ML production system.