The Muara Karang Generation Unit in North Jakarta is located in a coastal area that is highly vulnerable to climate change, particularly due to rising ambient air temperatures, sea-level rise, and coastal inundation. These impacts have affected the plant’s operational performance, including reduced efficiency of gas and steam turbines, increased cooling system loads, and the occurrence of seawater intrusion within the power plant area. Such conditions have the potential to disrupt the reliability of electricity supply to the strategic areas of DKI Jakarta. Therefore, a comprehensive climate vulnerability assessment is required to evaluate the level of risk, as well as the technical and financial implications of climate change on power plant performance. This study employs the Climate Vulnerability Index (CVI) approach, which comprises three components: exposure, sensitivity, and adaptive capacity. Exposure analysis was conducted using historical data on ambient air temperature, sea surface temperature, and sea-level rise for the 1994–2024 period, along with CMIP6 climate projections for 2026–2060 under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios. Sensitivity was assessed based on reductions in generation capacity due to increased air and seawater temperatures, higher fuel consumption, and the risk of seawater intrusion. Adaptive capacity was evaluated through an assessment of existing climate change adaptation and mitigation measures implemented at the facility. All indicators were normalized and weighted to produce a composite vulnerability index value. The results of the climate vulnerability assessment, based on the parameters of ambient temperature, sea temperature, and sea-level rise at the Muara Karang Power Generation Unit, show index values of 0.36 in 2030 and 0.45 in 2050, corresponding to “low” and “moderate” vulnerability categories, respectively.