The South Asian monsoon affects more than a billion people in the Indian subcontinent. The monsoon intraseasonal oscillation (MISO) determines the spatial structure of the monsoon rainfall on subseasonal timescales, and its accurate prediction is therefore key for agricultural and hydrological planning. Here, we combine data-driven forecasts of MISO with an ensemble of dynamical forecasts of the full system, leveraging the predictability of MISO to improve monsoon forecasts. Our results show significant improvement compared to state-of-the-art dynamical model forecasts, demonstrating the potential of data-driven forecasts to improve subseasonal monsoon prediction.