The exciton dynamics in monolayer black phosphorus is investigated over a very wide range of photoexcited exciton densities using time resolved photoluminescence. At low excitation densities, the exciton dynamics is successfully described in terms of a double exponential decay. With increasing exciton population, a fast, nonexponential component develops as exciton-exciton annihilation takes over as the dominant recombination mechanism under high excitation conditions. Our results identify an upper limit for the injection density, after which exciton-exciton annihilation reduces the quantum yield, which will significantly impact the performance of light emitting devices based on single-layer black phosphorus.