Recent observations have revealed that starburst galaxies can drive molecular gas outflows through stellar radiation pressure. Molecular gas is the phase of the interstellar medium from which stars form, so these outflows curtail stellar mass growth in galaxies. Previously known outflows, however, involve small fractions of the total molecular gas content and have typical scales of less than a kiloparsec. In at least some cases, input from active galactic nuclei is dynamically important, so pure stellar feedback (the momentum return into the interstellar medium) has been considered incapable of rapidly terminating star formation on galactic scales. Molecular gas has been detected outside the galactic plane of the archetypal starburst galaxy M82 (refs 4 and 5), but so far there has been no evidence that starbursts can propel substantial quantities of cold molecular gas to the same galactocentric radius (about 10 kiloparsecs) as the warmer gas that has been traced by metal ion absorbers in the circumgalactic medium. Here we report observations of molecular gas in a compact (effective radius 100 parsecs) massive starburst galaxy at redshift 0.7, which is known to drive a fast outflow of ionized gas. We find that 35 per cent of the total molecular gas extends approximately 10 kiloparsecs, and one-third of this extended gas has a velocity of up to 1,000 kilometres per second. The kinetic energy associated with this high-velocity component is consistent with the momentum flux available from stellar radiation pressure. This demonstrates that nuclear bursts of star formation are capable of ejecting large amounts of cold gas from the central regions of galaxies, thereby strongly affecting their evolution by truncating star formation and redistributing matter.