The Global Risk Report (2021) identifies ESG risks as the number one risk faced by the global economy. Banks have contributed to this risk and can also contribute to mitigating it. High exposure of Banks to ESG risks will contribute to climate disaster, which in turn will have financial risk implications for banks in the form of disaster events risks and energy transition risks. Depositors can discipline banks in reducing and preferably eliminating their ESG risks through enforcing market discipline by deposit withdrawal. This thesis investigates the extent to which deposit withdrawal works as market discipline against ESG risks in the banks of the OIC region. The thesis also examines the impact of financial risk represented by CAMELS variables on depositors' behavior. The generalized method of moments (System GMM estimator) is used for dynamic panel data models, as well as a sample from 65 countries over the period 2007 to 2016. Our findings indicate that depositors react significantly to environmental and governance risks while depositors' discipline does not exist with social risks. With regard to financial risks, our findings suggest weak evidence of market discipline. However, regressing CAMELS components separately provides better results and understanding than regressing CAMELS components collectively. In the OIC region, the study indicates that depositors tend to be sensitive to changes in capital adequacy, bank earnings and ESG risks, while in the non-OIC region, depositors are only sensitive to management quality.