Unreinforced masonry (URM) buildings are highly vulnerable to seismic ground motion, calling for quantitative risk assessment and mitigation programmes in different earthquake‐prone countries to reduce future losses. Despite the effectiveness of base isolation technology in reducing seismic response of buildings, the high costs of conventional isolators prevent their application to low‐cost housing in developing countries. Fiber‐reinforced elastomeric isolators (FREIs) have been recently developed as low‐cost isolators suitable for application to URM buildings. The structural performance assessment of base isolated URM buildings using FREIs can be a sustainable solution for a large‐scale mitigation of seismic risk. In this context, the present study presents the seismic fragility analysis of both fixed‐base and base‐isolated URM buildings. Five URM building archetypes were considered to account for variation in geometry and building configuration. A number of static pushover analyses and nonlinear time history analyses were carried out to assess the capacity and demand of the selected buildings, respectively, while considering the uncertainties associated with material properties, capacity model, damage state and earthquake ground motion. The fragility curves were developed for both fixed‐base and base‐isolated configurations of the different archetypes. The results show that the probability of slight to moderate damage to fixed‐base URM buildings is significantly higher than their base‐isolated counterparts, demonstrating that FREIs significantly improve their seismic performance. These outcomes address further research in promoting the development of FREIs to reduce the vulnerability of URM buildings in developing countries.