We observed Hubble Deep Field South with the new panoramic integral-field spectrograph MUSE that we built and have just commissioned at the VLT. The data cube resulting from 27h of integration covers one arcmin^2^ field of view at an unprecedented depth with a 1{sigma} emission-line surface brightness limit of 1x10^-19^erg/s/cm2/arcsec2, and contains ~90000 spectra. We present the combined and calibrated data cube, and we performed a first-pass analysis of the sources detected in the Hubble Deep Field South imaging. We measured the redshifts of 189 sources up to a magnitude I_814_=29.5, increasing the number of known spectroscopic redshifts in this field by more than an order of magnitude. We also discovered 26 Ly{alpha} emitting galaxies that are not detected in the HST WFPC2 deep broad-band images. The intermediate spectral resolution of 2.3{AA} allows us to separate resolved asymmetric Ly{alpha} emitters, [OII]3727 emitters, and [CIII]1908 emitters, and the broad instantaneous wavelength range of 4500{AA} helps to identify single emission lines, such as [OIII]5007, H{beta}, and H{alpha}, over a very wide redshift range. We also show how the three-dimensional information of MUSE helps to resolve sources that are confused at ground-based image quality. Overall, secure identifications are provided for 83% of the 227 emission line sources detected in the MUSE data cube and for 32% of the 586 sources identified in the HST catalogue. The overall redshift distribution is fairly flat to z=6.3, with a reduction between z=1.5 to 2.9, in the well-known redshift desert. The field of view of MUSE also allowed us to detect 17 groups within the field. We checked that the number counts of [OII]3727 and Ly{alpha} emitters are roughly consistent with predictions from the literature. Using two examples, we demonstrate that MUSE is able to provide exquisite spatially resolved spectroscopic information on the intermediate-redshift galaxies present in the field. This unique data set can be used for a wide range of follow-up studies. We release the data cube, the associated products, and the source catalogue with redshifts, spectra, and emission-line fluxes.