New Spitzer imaging observations have revealed the structure around the Mira variable star R Hya to be a one-sided parabolic arc 100 arcsec to the West stretching from North to South. We successfully model R Hya and its surroundings in terms of an interaction of the stellar wind from an asymptotic giant branch (AGB) star with the interstellar medium (ISM) the star moves through. Our three-dimensional hydrodynamic simulation reproduces the structure as a bow shock into the oncoming ISM. We propose this as another explanation of detached shells around such stars which should be considered alongside current theories of internal origin. The simulation predicts the existence of a tail of ram-pressure-stripped AGB material stretching downstream. Indications for such a tail behind R Hya are seen in IRAS maps.