Earthquakes are the leading natural disasters that seriously affect human life. Furthermore, earthquakes are natural disasters that have the ability to trigger a second disaster in addition to the damages they cause. From this point of view, post-earthquake fires are defined as the one of the most dangerous secondary disasters after an earthquake and often cause even more serious dangers. For this reason, government officials and relevant decision-makers should effectively determine post-earthquake fire risks and take necessary precautions. In this study, we consider the problem of determining the fire risk after an earthquake as a multi-criteria decision problem and present a two-level framework for risk assessment. The main and sub-criteria are determined by a detailed literature review and Modified Delphi method is employed to gain and consolidate expert opinions. Firstly, the importance weights of the criteria for post-earthquake fire risk problem are determined by the interval valued neutrosophic-Analytical Hierarchy Process (IVN-AHP) methodology. Then, interval valued neutrosophic TOPSIS (IVN-TOPSIS) method is used to rank the districts in Anatolian side of Istanbul according to their post-earthquake fire risks. The proposed risk assessment methodology is utilized with real life data to determine the most risky districts of Istanbul, Turkey. The result of proposed methodology is tested and validated with sensitivity analysis. A comparative analysis also is conducted to further validate the robustness and effectiveness of the proposed methodology. The proposed integrated methodology is intended to be a useful tool for risk assessment and to provide decision makers with a reliable assessment.