Aims: We explore the capabilities of CARMENES for characterising hot-Jupiter atmospheres by targeting multiple water bands, in particular, those at 1.15 and 1.4 μm. Hubble Space Telescope observations suggest that this wavelength region is relevant for distinguishing between hazy and/or cloudy and clear atmospheres. Methods: We observed one transit of the hot Jupiter HD 189733 b with CARMENES. Telluric and stellar absorption lines were removed using SYSREM, which performs a principal component analysis including proper error propagation. The residual spectra were analysed for water absorption with cross-correlation techniques using synthetic atmospheric absorption models. Results: We report a cross-correlation peak at a signal-to-noise ratio (S/N) of 6.6, revealing the presence of water in the transmission spectrum of HD 189733 b. The absorption signal appeared slightly blueshifted at -3.9 ± 1.3 km s-1. We measured the individual cross-correlation signals of the water bands at 1.15 and 1.4 μm, finding cross-correlation peaks at S/N of 4.9 and 4.4, respectively. The 1.4 μm feature is consistent with that observed with the Hubble Space Telescope. Conclusions: The water bands studied in this work have been mainly observed in a handful of planets from space. Being able also to detect them individually from the ground at higher spectral resolution can provide insightful information to constrain the properties of exoplanet atmospheres. Although the current multi-band detections can not yet constrain atmospheric haze models for HD 189733 b, future observations at higher S/N could provide an alternative way to achieve this aim.