We present ROSAT PSPC and HRI observations of the dwarf irregular galaxy Holmberg II (UGC 4305). This is one of the most luminous dwarf galaxies (L-X similar to 10(40) erg s(-1)) detected in the ROSAT All-Sky Survey. The X-ray emission comes from a single unresolved point source, coincident with a large HII region that emits intense radio emission. The source is variable on both year and day time-scales, clearly favouring accretion into a compact object rather than a supernova remnant or a superbubble interpretation for the origin of the X-ray emission. However, its X-ray spectrum is well-fitted by a steep power law or alternatively by a Raymond-Smith spectrum with kT similar to 0.8 keV, lower than the temperature of X-ray binaries in nearby spiral galaxies.