This study examines the relationship between the Madden‐Julian oscillation (MJO) and stratospheric quasi‐biennial oscillation (QBO) in a state‐of‐the‐art global numerical weather forecast model. A set of 61‐day model integrations, with 15 ensemble members, is performed across 84 start dates during December–February of 1989–2016. For 28 of those dates—every 1 January—the stratosphere is initialized from observation, and the model simulates stronger MJO events during observed easterly QBO phases (QBOE) than westerly QBO phases (QBOW). However, in these “control experiments,” the QBO's impact on the MJO is already present in the initial conditions, and the direct influence of the model stratosphere during the simulation is unclear. To explore this more directly, the model was rerun with an artificially imposed QBOE and QBOW state, replacing the existing stratospheric initial condition above 150 hPa while leaving the troposphere unaltered. Though the imposed QBO states weaken faster in the model than in observations, their persistence is comparable to the control simulations. The MJO is stronger during imposed‐QBOE experiments than imposed‐QBOW, and differences are statistically significant by several metrics, though magnitude of the differences is smaller than in observations. Analysis suggests that the strength of the MJO response to the QBO increases for simulations with stronger upper‐tropospheric temperature differences and for simulations in which the MJO at the initialization time is strong and active over the Maritime Continent. However, tropospheric conditions still appear to have a dominant effect in explaining the apparent QBO influence in this model.