The MATLAS deep imaging survey has uncovered a plethora of dwarf galaxies in the low density environment it has mapped. A fraction of them are unusually extended and have low surface brightness. Among these so-called ultra-diffuse galaxies, a few seem to host an excess of globular clusters (GCs). With the integral field unit spectrograph MUSE we have observed one of these galaxies – MATLAS J15052031+0148447 (MATLAS-2019) – located toward the nearby group NGC 5846 and measured its systemic velocity, age, and metallicity, and that of its GC candidates. For the stellar body of MATLAS-2019 we derive a metallicity of −1.33_−0.01^+0.19 dex and an age of 11.2_−0.8^+1.8 Gyr. For some of the individual GCs and the stacked GC population, we derive consistent ages and metallicities. From the 11 confirmed GCs and using a Markov Chain Monte Carlo approach we derived a dynamical mass-to-light ratio of 4.2_−3.4^+8.6 M_⊙/L_⊙. This is at the lower end of the luminosity-mass scaling relation defined by the Local Group dwarf galaxies. Furthermore, we could not confirm or reject the possibility of a rotational component in the GC system. If present, this would further modify the inferred mass. Follow-up observations of the GC population and of the stellar body of the galaxy are needed to assess whether this galaxy lacks dark matter, as was suggested for the pair of dwarf galaxies in the field of NGC 1052, or if this is a misinterpretation arising from systematic uncertainties of the method commonly used for these systems and the large uncertainties of the individual GC velocities.