Drone integration in sustainable agriculture has emerged as a transformative technological advancement, enabling farmers to achieve accurate crop health monitoring, soil analysis, weed mapping, precise spraying, and livestock monitoring. It facilitates many sustainable measures, such as conserving freshwater resources, reducing soil erosion and pesticide overuse, minimizing agriculture waste, and enhancing productivity and resilience. Despite its benefits, drone adoption faces several barriers, highlighting the requirement of well-structured mitigation strategies to overcome these challenges and ensure successful implementation. We propose a hybrid fuzzy-DEMATEL-MMDE-ISM-based approach for analysing the barriers to drone implementation in sustainable agriculture. We obtain a list of 15 potential barriers by exploring the relevant literature and finalizing the 13 critical barriers based on the experts' opinions. We adopt the fuzzy-Decision Making Trial and Evaluation Laboratory (fuzzy-DEMATEL) technique to segregate casual and effect barriers. Then, we apply the Maximum Mean De-Entropy (MMDE) method to determine the threshold value for the Interpretive Structural Modelling (ISM) method for constructing the three-level hierarchical structure of the barriers. The insights signify that the most crucial barriers are stability and reliability, drone sensor quality, and drone payload capacity. Flight duration, high initial cost, and maintenance infrastructure serve as linkage barriers between crucial barriers and public perception and psychological barrier. We also find some barriers with minimal or no interdependence on other barriers that should be handled separately. We suggest mitigation strategies to address the underlying challenges of drone implementation in sustainable agriculture. We can extend this study by incorporating additional barriers and applying different methods in other countries to examine the variations in the model.