Objective: The mechanisms of radiation-induced DNA damage can be understood via the fundamental acquisition of knowledge through a combination of experiments and modeling. Currently, most biological experiments are performed by irradiating an entire cell population, whereas modeling of radiation-induced effects is usually performed via Monte Carlo simulations with track structure codes coupled to realistic DNA geometries of a single-cell nucleus. However, the difference in scale between the two methods hinders a direct comparison because the dose distribution in the cell population is not necessarily uniform owing to the stochastic nature of the energy deposition. Thus, this study proposed the MINAS TIRITH tool to model the distribution of radiation-induced DNA damage in a cell population. Approach: The proposed method is based on precomputed databases of microdosimetric parameters and DNA damage distributions generated using the Geant4-DNA Monte Carlo Toolkit. First, a specific energy z was assigned to each cell of an irradiated population for a particular absorbed dose D_abs, following microdosimetric formalism. Then, each cell was assigned a realistic number of DNA damage events according to the specific energy z, respecting the stochastic character of its occurrence. Main results: This study validated the MINAS TIRITH tool by comparing its results with those obtained using the Geant4-DNA track structure code and a Geant4-DNA based simulation chain for DNA damage calculation. The different elements of comparison indicated consistency between MINAS TIRITH and the Monte Carlo simulation in case of the dose distribution in the population and the calculation of the amount of DNA damage. Significance: MINAS TIRITH is a new approach for the calculation of radiation-induced DNA damage at the cell population level that facilitates reasonable simulation times compared to those obtained with track structure codes. Moreover, this tool enables a more direct comparison between modeling and biological experimentation.