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 conventional (single or colloidal) dye molecules and quantum dots. In this paper, we verify 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 a 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 10 times that 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 unique direction for developing fast and efficient optoelectronic devices.