Lower atmospheric global dust storms affect the small‐ and large‐scale weather and variability of the whole Martian atmosphere. Analysis of the CO2 density data from the Neutral Gas and Ion Mass Spectrometer instrument on board NASA's Mars Atmosphere Volatile EvolutioN (MAVEN) spacecraft show a remarkable increase of gravity wave (GW)‐induced density fluctuations in the thermosphere during the 2018 major dust storm with distinct latitude and local time variability. The mean thermospheric GW activity increases by a factor of two during the storm event. The magnitude of relative density perturbations is around 20% on average and 40% locally. One and a half months later, the GW activity gradually decreases. Enhanced temperature disturbances in the Martian thermosphere can facilitate atmospheric escape. For the first time, we estimate observationally that, for a 20% and 40% GW‐induced disturbances, the net increase of Jeans escape flux of hydrogen is a factor of 1.3 and 2, respectively. Plain Language Summary Atmospheric gravity waves play an important dynamical and thermodynamical role in coupling the different atmospheric layers, especially on Earth and Mars. Using data from NASA's Mars Atmosphere Volatile EvolutioN (MAVEN) mission, we study the effects of a planet‐encircling major dust storm on thermospheric gravity wave activity and observationally estimate for the first time a potential influence of gravity waves on atmospheric escape on Mars. Gravity wave activity measured in terms of relative density fluctuations increases by a factor of two during the peak phase of the storm. We show that larger‐amplitude gravity waves facilitate atmospheric escape of hydrogen from Mars' upper atmosphere. For 40% gravity wave‐induced relative disturbances of temperature, the net escape rate doubles. Key Points Thermospheric gravity wave activity doubles during the dust storm Gravity wave induced density fluctuations in the thermosphere are up to 40% during the peak storm phase Gravity waves significantly increase hydrogen escape flux by modulating temperature fluctuations