We mapped the Galactic young massive star cluster Westerlund 2 (Wd2) with the integral field spectrograph MUSE (spatial resolution: 0.2 arcsec px −1 , spectral resolution: ∆λ = 1.25Å, wavelength range 4600-9350Å) mounted on the VLT, as part of an on-going study to measure the stellar and gas kinematics of the cluster region. In this paper we present the fully reduced dataset and introduce our new Python package "MUSEpack", which we developed to measure stellar radial velocities with an absolute precision of 1-2 km s −1 without the necessity of a spectral template library. This novel method uses the two-dimensional spectra and an atomic transition line library to create templates around strong absorption lines for each individual star. The code runs fully automatically on multi-core machines, which makes it possible to efficiently determine stellar radial velocities of a large number of stars with the necessary precision to measure the velocity dispersion of young star clusters. MUSEpack also provides an enhanced method for removing telluric lines in crowded fields without sky exposures and a Python wrapper for ESO's data reduction pipeline.We observed Wd2 with a total of 11 short and 5 long exposures to cover the bright nebular emission and OB stars, as well as the fainter pre-main sequence stars down to ∼ 1 M . The survey covers an area of ∼ 11 arcmin 2 (15.8 pc 2 ). In total, we extracted 1,725 stellar spectra with a mean S/N> 5 per pixel. A typical radial velocity (RV) uncertainty of 4.78 km s −1 , 2.92 km s −1 , and 1.1 km s −1 is reached for stars with a mean S/N> 10, S/N> 20, S/N> 50 per pixel, respectively. Depending on the number of spectral lines used to measure the RVs, it is possible to reach RV accuracies of 0.9 km s −1 , 1.3 km s −1 , and 2.2 km s −1 with ≥ 5, 3-4, and 1-2 spectral lines, respectively. The combined statistical uncertainty on the radial velocity measurements is 1.10 km s −1 .