  We mapped the Galactic young massive star cluster Westerlund 2 (Wd2) with the
integral field spectrograph MUSE (spatial resolution: 0.2arcsec/px, spectral
resolution: $\Delta \lambda$ = 1.25A, wavelength range 4600-9350A) 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 1-2km/s 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 ~1M$_\odot$. The survey covers an area
of ~11arcmin$^2$ (15.8pc$^2$). In total, we extracted 1,725 stellar spectra
with a mean S/N>5 per pixel. A typical radial velocity (RV) uncertainty of
4.78km/s, 2.92km/s, and 1.1km/s 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
0.9km/s, 1.3km/s, and 2.2km/s with $\geq5$, 3-4, and 1-2 spectral lines,
respectively. The combined statistical uncertainty on the radial velocity
measurements is 1.10km/s.
