The threat of fire after an earthquake can substantially amplify the structural damage, which may lead to higher losses compared to a single seismic event. Usually, 2D fragility curves are used to evaluate the potential damage that may occur to structures after an earthquake. However, in the case of post-earthquake fire (PEF), 3D fragility surfaces can be more effective tools as they display the combined effect of two hazards for damage assessment. Thus, in this study, the vulnerability of a 4-story steel moment-resisting frame (SMRF) exposed to PEF is investigated. This study highlights the critical importance of PEF fragility assessment for this building type as it is currently lacking in literature. The SMRF is modeled using OpenSees and the 3D fragility surfaces are developed by considering both demand and capacity parameters as random variables, generated using Latin hypercube sampling. After defining randomness in the characteristics of the examined building, 15 acceleration time histories are applied via the multiple stripe analysis to simulate the earthquake. Subsequently, the fire is simulated in the corner bay of the first floor to investigate the vulnerability of the earthquake-damaged column exposed to fire. To create a more realistic model, heat is transferred to all beams and columns in the exposed bay via convection, radiation, and conduction. The results indicate that the occurrence of PEF elevates the probability of damage when contrasted with either the earthquake or fire. Furthermore, the potential for significant variations in fragilities with different limit states is highlighted. The findings of this study can be useful in addressing the structural risk due to PEF, which is an aspect that has not been considered in the current seismic design codes.