Due to much lower initial and operating costs, as well as a great environmental and energy performance, there has been a growing tendency towards the application of solar still desalination systems to deal with water scarcity issues. By taking advantage of higher investments and providing incentives to policy makers, the application could be even broader. In order to convince the policy makers and investors, it is important to provide a clear and realistic overview of the technical, economic, and environmental viability of solar stills, and several studies have evaluated them from different viewpoints. Nonetheless, the economic and environmental factors have uncertainties, which have not been taken into account. Therefore, this study uses the Monte Carlo approach to consider the effects of the uncertainty of inflation and discount rates, in addition to emission factors, on the system’s techno-enviro-economic viability. The study is performed by covering cost per liter (CPL) and the annual saving of CO2 (SCO2) as the most important key techno-economic and environmental indicators of the system. The results show that the best probability distribution functions for inflation, discount, and emission factors are normal, log-normal, and their summation, respectively. Furthermore, both SCO2 and CPL are found to have considerable uncertainty. The former has a variation ranging from 317.7 to 427.9 g, while the corresponding values for the latter are 0.0212 to 0.0270 $ · L−1, respectively. With the amounts of 0.1716 and 0.1727, the values of 378.9 g and 0.0245 $ · L−1 are the values with the highest chance of occurrence for SCO2, as well as for CPL, respectively.