We present ROSAT HRI X-ray data and optical imaging of the important dwarf starburst Markarian 33 . We find an extended , complex , shell-like morphology in the X-ray emission , with an extent of \sim 2.3 \times 1.9 kpc , coincident with the bright star-forming regions at the centre of the galaxy . The physical extent of this X-ray emission from Mrk 33 is very similar to the observed H \alpha emission , and suggests that the bulk of the X-ray emission is coming from an expanding superbubble . We estimate the age and mass of Mrk 33 ’ s starburst to be 5.8 Myr and 6.9 \times 10 ^ { 6 } M _ { \odot } respectively with the energy injection rate in the central regions of the galaxy being \sim 10 ^ { 41 } erg s ^ { -1 } , while the associated mass-loss rate from the star-forming regions is estimated to be \sim 0.2 M _ { \odot } yr ^ { -1 } . We suggest that the X-ray emission is predominantly powered by starburst type activity and argue that a blowout in the form of a galactic wind is the most likely fate for Mrk 33 resulting in the loss of most of the galaxy ’ s metal-enriched material and a small fraction ( < 1 per cent ) of the ISM .