Understanding the interactions between shallow saline groundwater and surface water is crucial for managing water logging in deltaic islands. Water logging conditions result in the accumulation of salt in the root zone of crops and detrimentally affect agriculture in the economically and socially backward deltaic region of West Bengal and Bangladesh. In this paper, we undertook a modeling study of surface water–groundwater interactions in the Gosaba Island of Sundarbans region of the Ganges delta using MODFLOW followed by comprehensive parameter sensitivity analysis. Further, scenario analyses (i.e., no-drain, single drain, three drains) were undertaken to evaluate the effectiveness of drainage infrastructure to reduce saline water logging conditions. The evaluation indicated that installation of three drains can remove water at a rate of up to −123.3 m3day−1 and lower the water table up to 0.4 m. The single drain management scenario could divert water at the rate of −77.9 m3day−1 during post monsoon season, lowering the shallow saline groundwater table up to 0.1 m. This preliminary modeling study shows encouraging results to consider drainage management as to solve the increasing challenge of water logging and salinity management in the deltaic region. The insights will be useful for farmers and policymakers in the region for planning various sustainable saline groundwater management. Building drainage infrastructure could potentially be part of initiatives like the national employment guarantee scheme in India. In the future, this model can be coupled with solute transport models for understanding the current status and future expansion of salinity in the study area. Further modeling and optimization analysis can help identify the optimal depth and spacing of drains.