Two-dimensional molecular aggregate (2DMA), a thin sheet of strongly interacting dipole molecules self-assembled at close distance on an ordered lattice, is a fascinating fluorescent material. It is distinctively different from the single or colloidal dye molecules or quantum dots in most previous research. In this paper, we verify for the first time that when a 2DMA is placed at a nanometric distance from a metallic substrate, the strong and coherent interaction between the dipoles inside the 2DMA dominates its fluorescent decay at picosecond timescale. Our streak-camera lifetime measurement and interacting lattice-dipole calculation reveal that the metal-mediated dipole-dipole interaction shortens the fluorescent lifetime to about one half and increases the energy dissipation rate by ten times than expected from the noninteracting single-dipole picture. Our finding can enrich our understanding of nanoscale energy transfer in molecular excitonic systems and may designate a new direction for developing fast and efficient optoelectronic devices.