The electron capture process was studied for Xe$^{54+}$ colliding with H$_2$ molecules at the internal gas target of the ESR storage ring at GSI, Darmstadt. Cross section values for electron capture into excited projectile states were deduced from the observed emission cross section of Lyman radiation, being emitted by the hydrogen-like ions subsequent to the capture of a target electron. The ion beam energy range was varied between 5.5 MeV/u and 30.9 MeV/u by applying the deceleration mode of the ESR. Thus, electron capture data was recorded at the intermediate and in particular the low collision energy regime, well below the beam energy necessary to produce bare xenon ions. The obtained data is found to be in reasonable qualitative agreement with theoretical approaches, while a commonly applied empirical formula significantly overestimates the experimental findings.