This paper investigates how climate shocks affect banking stability in a large panel of 1208 banks observed at annual frequency over the period 2005-2019 for 16 Latin American countries. We use strong El Niño Southern Oscillation (ENSO) events as a natural experiment for climate shocks related to climate change, as they produce quasi-periodic climate oscillations that can lead to unpredictable natural disasters. Our results show that, when considering Latin American countries, weather shocks associated with strong ENSO events can have adverse financial consequences that lead to a decline in banking stability. We also reveal that strong El Niño and La Niña shocks have asymmetrical effects on banking stability. Strong El Niño shocks are associated with lower banks' stability, resulting from decreased performances associated with increased credit and liquidity risks. In contrast, strong La Niña shocks appear to have economic benefits, with no significant impact on banking stability, but higher banks' performances and lower credit risk. Finally, further estimates identify some key characteristics of "climate-resilient banks". Banks with a larger size, a higher capital ratio, and less market-oriented activities are more resilient to adverse climate shocks resulting from ENSO events. As climate change should intensify the frequency and magnitude of ENSO's cyclical pattern, these findings can help estimate the potential adverse effects of climate change-induced physical risks on banking stability and inform future mitigation and adaptation policies.