The Asmari reservoir in southwest Iran has been producing oil continuously for over 50 years. However, due to an essential pressure decline, the reservoir is now a potential candidate for injection projects. The geomechanical analysis is essential for a successful injection operation to enhance reservoir production and address possible challenges. An accurate estimation of the injection pressure is necessary to maintain optimal conditions during the injection process and reduce possible risks. In this work, a coupled reservoir-geomechanical model, as well as rock mechanical tests, is performed to evaluate not only pressure variation and the associated in situ stress changes but also their potential influences on fault reactivation, reservoir–caprock stability, and surface displacement. For geomechanical evaluation, empirical correlations are derived between static and dynamic rock properties based on core data and existing petrophysical logs for the studied reservoir–caprock system. Based on the hydro-mechanical results, the maximum displacement is limited to the vicinity of the injection wells, where the highest pressure changes occur. The geomechanical analysis of the reservoir–caprock system shows that this system is stable until the injection pressure reaches 4.3× the initial reservoir pressure. Also, the injection pressure is not high enough to compromise the integrity of faults, indicating that the loading on the fault planes is too low to reactivate the pre-existing faults. The approach followed in this study can be applied to future field development strategies and feasibility considerations for CO2 sequestration and underground gas storage projects.