Context. The dynamical mass-to-light (M/L) ratios of massive ultra-compact dwarf galaxies (UCDs) are about 50% higher than predicted by stellar population models. Aims. Here we investigate the possibility that these apparently elevated M/L ratios of UCDs are caused by a central black hole (BH) that heats up the internal motion of stars. We focus on a sample of ∼50 extragalactic UCDs from the literature for which velocity dispersions and structural parameters have been measured. Methods. To be self-consistent in our BH mass estimates, we first redetermine the dynamical masses and M/L ratios of our sample UCDs, using up-to-date distance moduli and a consistent treatment of aperture and seeing effects. On average, the homogeneously redetermined dynamical mass and M/L ratios agree to within 5% with previous literature results. We calculate the ra-pop between the dynamical and the stellar population M/L for an assumed age of 13 Gyr. Ψ > 1 indicates an elevated dynamical M/L ratio, suggesting dark mass on top of a canonical stellar population of old age. For all UCDs with Ψ > 1 we estimate the mass of a hypothetical central black hole needed to reproduce the observed integrated velocity dispersion Results. Massive UCDs (M > 10 7 M ) have an average Ψ = 1.7 ± 0.2, implying notable amounts of dark mass in them. We find that, on average, central BH masses of 10-15% of the UCD mass can explain these elevated dynamical M/L ratios. The implied BH masses in UCDs range from several 10 5 M to several 10 7 M . In the M BH -luminosity plane, UCDs are offset by about two orders of magnitude in luminosity from the relation derived for galaxies. Our findings can be interpreted such that massive UCDs originate from progenitor galaxies with masses around ∼10 9 M , and that those progenitors have SMBH occupation fractions of ∼60-100%. The suggested UCD progenitor masses agree with predictions from the tidal stripping scenario. Also, the typical BH mass fractions of nuclear clusters in such ∼10 9 M galaxy bulges agree with the 10-15% BH fraction estimated for UCDs. Lower-mass UCDs (M < 10 7 M ) exhibit a bimodal distribution in Ψ, suggestive of a coexistence of massive globular clusters and tidally stripped galaxies in this mass regime. Conclusions. Central BHs as relict tracers of tidally stripped progenitor galaxies are a plausible explanation for the elevated dynamical M/L ratios of UCDs. Direct observational tests of this scenario are suggested.