The variables of sustainable agricultural indicators have inherent risk and uncertainty; therefore, neglecting them leads to unrealistic results. Hence, this study aims to assess agricultural sustainability indices by accounting for risk factors, including yield, price fluctuations, and chemical fertilizer and herbicide use, in wheat production across Iranian provinces during 2000-2018. First, economic, environmental, and economic-environmental indices by considering risk for the wheat producers were calculated. The CRITIC method was applied to determine the weights of indicators, and finally, the stochastic dominance methods (SSD and SDRF) were used to rank provinces based on their economic, environmental, and economic-environmental sustainability indices. The results showed that provinces located in the center and south (e.g. Khuzestan, Isfahan, and Fars) are in a high-risk group, those in the west and semi-arid areas (e.g. Kermanshah, Semnan, and Hamedan) fall into a moderate-risk group, and provinces in the north (e.g. Mazandaran, Sistan and Baluchestan, and Kohgiluyeh and Boyer-Ahmad) exhibit low risk. These findings indicate regional disparities in sustainability conditions. Therefore, risk-based management policies, including region-specific support measures, irrigation improvements, and input optimization, are essential to promote the sustainable production of wheat across Iran.