Multiphysics modeling of a planar HgCdTe-based mid-wavelength infrared (MWIR) focal plane array with $3\,\mu$m-wide pixels enlightens the role of surface plasmon-polaritons observed in gold nanorods arranged on its illuminated face. Simulations indicate that the proposed plasmonic detector, which employs a $1\,\mu$m-thick absorber layer, exhibits a reduction of diffusive inter-pixel crosstalk by more than one order of magnitude with respect to more conventional, non-plasmonic detectors with a $5\,\mu$m-thick absorber layer, without penalizing responsivity and achieving increased detectivity in the whole MWIR band by taking advantage of the absorber volume reduction.