Mira is one of the first variable stars ever discovered and it is the prototype (and also the nearest example) of a class of low-to-intermediate-mass stars in the late stages of stellar evolution. These stars are relatively common and they return a large fraction of their original mass to the interstellar medium (ISM) (ref. 2) through a processed, dusty, molecular wind. Thus stars in Mira's stage of evolution have a direct impact on subsequent star and planet formation in their host galaxy. Previously, the only direct observation of the interaction between Mira-type stellar winds and the ISM was in the infrared. Here we report the discovery of an ultraviolet-emitting bow shock and turbulent wake extending over 2 degrees on the sky, arising from Mira's large space velocity and the interaction between its wind and the ISM. The wake is visible only in the far ultraviolet and is consistent with an unusual emission mechanism whereby molecular hydrogen is excited by turbulent mixing of cool molecular gas and shock-heated gas. This wind wake is a tracer of the past 30,000 years of Mira's mass-loss history and provides an excellent laboratory for studying turbulent stellar wind-ISM interactions.