The excitonic luminescence of monolayer molybdenum disulfide (MoS2) on a gold substrate is studied by scanning tunneling microscopy (STM). STM-induced light emission (STM-LE) from MoS2 is assigned to the radiative decay of A and B excitons. The intensity ratio of A and B exciton emission can be modulated by the tunneling current, since the A exciton emission intensity saturates at high tunneling currents. Moreover, the corrugated gold substrate introduces local strain to the monolayer MoS2, resulting in significant changes of electronic bandgap and valence band splitting. The modulation rates of strain on A and B exciton energies are estimated as -72 meV/% and -57 meV/%, respectively. STM-LE provides a direct link between exciton energy and local strain in monolayer MoS2 with a spatial resolution <10 nm.