Masonry minarets constitute an important component of Islamic architectural heritage. In seismically active regions like Southwest Asia and Mediterranean countries, historically, minarets are severely damaged and collapsed during earthquakes. Due to vast geometric diversity, their seismic analysis needs to consider typological variation and seismic performance. The literature on seismic vulnerability of minarets is heavily concentrated on singular case studies analysed by sophisticated numerical approaches, while there is a lack of a comprehensive approach both in the scientific community and the building codes and preservation guidelines. Thus, the seismic vulnerability assessment of masonry minarets presents challenges that require both computational efficiency and typological diversity. This research aims to develop a computational framework for the seismic vulnerability assessment of masonry minarets by a geometry parametrization system which translates minaret data into computable models evaluated through Limit Analysis approach. Minaret3D, a novel parametric tool is developed to analyse 3D geometries of diverse minaret typologies ranging from Turkey, Greece, Macedonia, Bosnia and Herzegovina to Egypt and Iran. In Minaret3D, a rule-based engine leverages documented historical data to systematically vary geometric parameters (such as slenderness ratios and segment dimensions) and material properties, creating a representative ensemble of virtual minaret structures. In the second stage, an integrated computational workflow couples the Minaret3D with Limit Analysis approach based on predefined collapse mechanisms. With this approach, it is possible to both perform analysis on existing minaret structures, and to obtain seismic behavior patterns and design constraints within ranges according to seismic safety for future constructions. This paper discusses the development of the framework, the calibration of the sensitivity analysis constraints, and the resulting catalogue of virtual models, offering a significant contribution to the preservation of large number of heritage minaret structures in seismically active regions.