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A reliable projection of future South Asian summer monsoon (SASM) benefits a large population in Asia. Using a 100-member ensemble of simulations by the Max Planck Institute Earth System Model (MPI-ESM) and a 50-member ensemble of simulations by the Canadian Earth System Model (CanESM2), we find that internal variability can overshadow the forced SASM rainfall trend, leading to large projection uncertainties for the next 15 to 30 years. We further identify that the Interdecadal Pacific Oscillation (IPO) is, in part, responsible for the uncertainties. Removing the IPO-related rainfall variations reduces the uncertainties in the near-term projection of the SASM rainfall by 13 to 15% and 26 to 30% in the MPI-ESM and CanESM2 ensembles, respectively. Our results demonstrate that the uncertainties in near-term projections of the SASM rainfall can be reduced by improving prediction of near-future IPO and other internal modes of climate variability.