Naturally fractured reservoirs (NFRs), such as fractured carbonate reservoirs, are ubiquitous across the worldwide and are potentially very good source to store carbondioxide (CO2) for a longer period of time. The simulation models are great tool to assess the potential and understanding the physics behind CO2-brine interaction in subsurface reservoirs. Simulating the behavior of fluid flow in NFR reservoirs during CO2 are computationally expensive because of the multiple reasons such as highly-fractured and heterogeneous nature of the rock, fast propagation of CO2 plume in the fracture network, and high capillary contrast between matrix and fractures. This paper presents a data-driven deep learning surrogate modeling approach that can accurately and efficiently capture the temporal-spatial dynamics of CO2 saturation plumes during injection and post-injection monitoring periods of Geological Carbon Sequestration (GCS) operations in NFRs. We have built a physics-based numerical simulation model to simulate the process of CO2 injection in a naturally fractured deep saline aquifers. A standalone package was developed to couple the discrete fracture network in a fully compositional numerical simulation model. Then reservoir model was sampled using the Latin-Hypercube approach to account for a wide range of petrophysical, geological, reservoir, and operational parameters. The simulation model parameters were obtained from extensive geological surveys published in literature. These samples generated a massive physics-informed database (about 900 simulations) that provides sufficient training dataset for the Deep Learning surrogate models. Average Absolute Percentage Error (AAPE) and coefficient of determination (R2) were used as error metrics to evaluate the performance of the surrogate models. The developed workflow showed superior performance by giving AAPE less than 5% and R2 more than 0.95 between ground truth and predictions of the state variables. The proposed Deep Learning framework provides an innovative approach to track CO2 plume in a fractured carbonate reservoir and can be used as a quick assessment tool to evaluate the long term feasibility of CO2 movement in fractured carbonate medium.