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Context. After many attempts over more than a decade, high-resolution spectroscopy has recently delivered its first detections of molecular absorption in exoplanet atmospheres, both in transmission and thermal emission spectra. Targeting the combined signal from individual lines in molecular bands, these measurements use variations in the planet radial velocity to separate the planet signal from telluric and stellar contaminants. Aims. We apply high-resolution spectroscopy to probe molecular absorption in the day-side spectrum of the bright transiting hot Jupiter HD 189733b. Methods. We observed HD 189733b with the CRIRES high-resolution near-infrared spectograph on the Very Large Telescope during three nights, targeting possible absorption from carbon monoxide, water vapour, methane, and carbon dioxide, at 2.0 and 2.3 μm. Results. We detect a 5-σ absorption signal from CO at a contrast level of ~4.5 × 10-4 with respect to the stellar continuum, revealing the planet orbital radial velocity at 154+4-3 km s-1. This allows us to solve for the planet and stellar mass in a similar way as for stellar eclipsing binaries, resulting in 0.846+0.068-0.049M⊙ and Mp = 1.162+0.058-0.039 MJup. No significant absorption is detected from H2O, CO2, or CH4 and we determine upper limits on their line contrasts. Conclusions. The detection of CO in the day-side spectrum of HD 189733b can be made consistent with the haze layer proposed to explain the optical to near-infrared transmission spectrum if the layer is optically thin at the normal incidence angles probed by our observations, or if the CO abundance is high enough for the CO absorption to originate from above the haze. Our non-detection of CO2 at 2.0 μm is not inconsistent with the deep CO2 absorption from low-resolution NICMOS secondary eclipse data in the same wavelength range. If genuine, the absorption would be so strong that it blanks out any planet light completely in this wavelength range, leaving no high-resolution signal to be measured.