The Agri-Food Supply Chain (ASC) is crucial in delivering food, essential inputs, and other derived products. However, it faces significant challenges, including increasing food demand, ensuring quality and safety, and minimizing waste. Additionally, supply chains are highly susceptible to unpredictable events that can disrupt operations, with the ASC’s complexity making it particularly vulnerable. Effective risk management is, therefore, essential. This study examines the Persian Lemon ASC in the Citrus District of Martínez de la Torre, Veracruz, to identify potential risks and provide insights to support decision-makers in designing risk management strategies. Based on input from nine experts, 38 potential risks were identified and assessed, 24 external and 14 internal. The Analytical Hierarchy Process (AHP) was employed to determine severity-impact weights for each risk. Subsequently, the Risk Priority Level (RPL) was assessed using the Failure Mode and Effects Analysis (FMEA) technique. The most critical risks were associated with the supply of Persian Lemons. To enhance resilience and ensure continuity in the supply chain, it is essential to establish a strategic framework that prioritizes risk detection and mitigation while developing continuity plans.