Context. Atmospheric properties of exoplanets can be constrained with transit spectroscopy. At low spectral resolution, this technique is limited by the presence of clouds. The signature of atomic sodium (Na i), known to be present above the clouds, is a powerful probe of the upper atmosphere, where it can be best detected and characterized at high spectral resolution. Aims. Our goal is to obtain a high-resolution transit spectrum of HD 189733b in the region around the resonance doublet of Na i at 589 nm, to characterize the absorption signature that was previously detected from space at low resolution. Methods. We analyzed archival transit data of HD 189733b obtained with the HARPS spectrograph (ℛ = 115 000) at the ESO 3.6-m telescope. We performed differential spectroscopy to retrieve the transit spectrum and light curve of the planet, implementing corrections for telluric contamination and planetary orbital motion. We compared our results to synthetic transit spectra calculated from isothermal models of the planetary atmosphere. Results. We spectrally resolve the Na i D doublet and measure line contrasts of 0.64 ± 0.07% (D2) and 0.40 ± 0.07% (D1) and FWHMs of 0.52 ± 0.08 Å. This corresponds to a detection at the 10σ level of excess of absorption of 0.32 ± 0.03% in a passband of 2 × 0.75 Å centered on each line. We derive temperatures of 2600 ± 600 K and 3270 ± 330 K at altitudes of 9800 ± 2800 and 12 700 ± 2600 km in the Na i D1 and D2 line cores, respectively. We measure a temperature gradient of ~0.2 K km-1 in the region where the sodium absorption dominates the haze absorption from a comparison with theoretical models. We also detect a blueshift of 0.16 ± 0.04 Å (4σ) in the line positions. This blueshift may be the result of winds blowing at 8 ± 2 km s-1 in the upper layers of the atmosphere. Conclusions. We demonstrate the relevance of studying exoplanet atmospheres with high-resolution spectrographs mounted on 4-m-class telescopes. Our results pave the way for an in-depth characterization of physical conditions in the atmospheres of many exoplanetary systems with future spectrographs such as ESPRESSO on the VLT or HiReS and METIS on the E-ELT.