Water is predicted to be among the most abundant (if not the most abundant) molecular species after hydrogen in the atmospheres of close-in extrasolar giant planets ('hot Jupiters'). Several attempts have been made to detect water on such planets, but have either failed to find compelling evidence for it or led to claims that should be taken with caution. Here we report an analysis of recent observations of the hot Jupiter HD 189733b (ref. 6) taken during the transit, when the planet passed in front of its parent star. We find that absorption by water vapour is the most likely cause of the wavelength-dependent variations in the effective radius of the planet at the infrared wavelengths 3.6 mum, 5.8 mum (both ref. 7) and 8 mum (ref. 8). The larger effective radius observed at visible wavelengths may arise from either stellar variability or the presence of clouds/hazes. We explain the report of a non-detection of water on HD 189733b (ref. 4) as being a consequence of the nearly isothermal vertical profile of the planet's atmosphere.