To constrain the poroelastic component of postseismic deformation, we model the subsurface hydrologic response to the Mw 7.6 subduction zone earthquake that occurred on the plate interface beneath the Nicoya peninsula in Costa Rica on 5 September 2012. The model shows that poroelastic relaxation occurs on multiple time scales and the associated deformation can be up to 2 cm for the trench‐perpendicular component. By modeling the time‐dependent deformation associated with poroelastic relaxation, we can begin to remove its contribution from the observed geodetic signal. Inversions for after slip that ignore poroelastic deformation have errors of 10–20% overall and up to 50% locally. Poroelastic effects can both mute and amplify the inferred afterslip.