Internal gravity waves influence a variety of phenomena in Earth’s stratosphere and upper troposphere, including aviation weather turbulence and circulations that set high-altitude distributions of ozone and greenhouse gases. Here coupling between the dominant mode of subseasonal variability of the equatorial atmosphere - the Madden-Julian oscillation (MJO) - and subtropical stratospheric gravity waves created by flow over topography is documented for the first time. We use three different meteorological data sets to show that during boreal winter, the MJO modifies the vertical distribution of internal gravity wave drag induced by the Tibetan Plateau and the deposition of momentum into the stratosphere. This interaction, however, has no significant impact on the vertically integrated wave drag. Our findings raise new questions about how future changes in tropical rainfall might affect stratospheric variability and highlight the importance of local processes over Tibet for the circulations that set distributions of climatically important high-altitude trace gases.