This paper studies the relationship between financial stability and sustainable development from the fiscal and monetary policy perspective in 33 developing countries and 7 developed countries in the period 2005–2020. Bayesian regression results show that financial stability positively affects sustainable development in both groups of countries with a low probability of impact. This probability is above 79.3% in developed countries and above 81.5% in developing ones. When considering the role of monetary policy, the direction of impact and probability is different. Specifically, financial stability in the environment of high inflation and increased money supply (ZscoreInf and ZscoreM2) negatively affects sustainable development in both country groups with high probabilities. In contrast, when considering the monetary policy with the foreign exchange reserves tool (ZscoreER), financial stability positively impacts sustainable development with the probability of 89.6% in developed countries and 92.5% in developing one. When considering the role of fiscal policy, financial stability with government spending (ZscoreGE) positively affects sustainable development with a probability of over 99.7% in the two groups of countries. Meanwhile, tax income in a financially stable environment increases the probability of a positive effect at 100% in developed countries, and a negative effect with a probability of 60.9% in developing countries. From the above results, we propose that central banks in both developed and developing countries should aim to stabilize prices and aim to maintain a low inflation rate to help limit shocks to sudden interest rate changes that cause market volatility. This is a premise to help stabilize finance and promote sustainable development. Furthermore, these countries should maintain an adequate foreign exchange reserve to withstand external shocks and ensure they have enough foreign currency to meet macroeconomic needs, which can boost confidence.