The seismic history of the Mosha fault, the largest and most active fault of Eastern Tehran metropolis, and its relation to the Damavand active volcano, the highest mountain in the Middle East, is investigated. We deduce that the central Mosha, near the Damavand, has a higher seismicity than either its western or eastern segments. On 7 May 2020, an Mw 5.1 earthquake occurred on the central Mosha, about 40 km east of Tehran and 10 km southwest of the Damavand crest, and it was felt intensely in Tehran. Its rupture is imaged and located in a region that presented a relative seismic quiescence compared to its eastern and western parts, during the last 14 years, suggesting its partial locking and heterogeneous distribution of fault frictional strength on this segment of Mosha. Its significant directivity to the west is confirmed by the mainshock rupture model, its PGA distribution, and distribution of early aftershocks. The rupture model suggests a relatively small stress drop of 2.6 bar, which is consistent with the comparatively high rupture dimension of 9 km for a Mw 5.1 earthquake, and indicates the easy rupture expansion on the central Mosha near the Damavand Volcano. The central Mosha experienced earthquakes in 1930, 1955, and 1983, as well as high microseismic activity and the 2020 seismic sequence, all of which strongly point to a possible influence of the Damavand Volcano on the seismicity of the central Mosha. This is corroborated by the observation of hydrothermal zones on the Mosha fault and the extension of a sill-like Damavand young magma chamber until central Mosha in tomography studies. We propose that the existing heat may increase the pore pressure on the fault, which lowers the effective normal stress, facilitates the nucleation-expansion of the rupture, and unclamps the fault. Damavand could act as a fuse and nucleate earthquakes, and if the rupture extends toward the west, it could have a significant directivity effect on low-frequency seismic waves that reach Tehran without attenuation and affect tall structures. In addition, high site amplification for frequencies up to 16 Hz due to the deep sedimentary basin, mainly in the mid-city of Tehran, will be remarkable for short buildings.