This work sheds light into the effect of the periodic pattern of bricks and mortar joints on the stress transfer at the interface between fiber-reinforced polymer (FRP) composites and masonry. Experimental evidence is used to highlight that the fracture process at the FRP-masonry interface depends on the characteristics of the constituent materials and the geometry of the masonry. Two simplified cohesive material laws are proposed for the FRP-brick and FRP-mortar interfaces, which are associated with finite effective bond lengths of the two interfaces. The aforementioned simplified interfacial laws are employed to compute the load response of the FRP-masonry interface, which is compared with the experimental one. The results indicate that length of the stress-transfer zone of, and the transferable load at, the FRP-masonry interface vary periodically in accordance with the periodic pattern of bricks and mortar joints.