We explore two possible scenarios to explain the observed γ-ray emission associated with the atypical globular cluster ω-Centauri: emission from millisecond pulsars (MSP) and dark matter (DM) annihilation. In the first case we predict the total number of MSPs in the globular cluster (n=45+22−16) using a new Bayesian method that combines the observational uncertainty in γ-ray counts with the intrinsic variation in individual pulsar luminosities. A DM interpretation is motivated by the possibility of ω-Centauri being the remnant core of an ancient dwarf galaxy hosting a surviving DM component. At least two annihilation channels, light quarks and muons, can plausibly produce the observed γ-ray spectrum. We are able to constrain the DM particle mass despite substantial uncertainties in the shape of the density profile (10 GeV ≲ mχ ≲ 30 GeV for annihilation into light quarks and 5 GeV ≲ mχ ≲ 9 GeV for annihilation into muons). We translate upper limits on ω-Centauri's remnant dark matter content into lower limits on the annihilation cross section (⟨ σ v⟩ ≳ 10−29 cm3 s −1 and ⟨ σ v⟩ ≳ 10−28 cm3 s −1 for quarks and muons respectively), taking into account the spatial extension of the DM halo. Moreover, there is a relatively small range of DM density profiles which are consistent with ω-Centauri's kinematics and stellar mass and can explain its γ-ray spectrum while simultaneously evading CMB constraints on dark matter annihilation. Further analysis of ω-Centauri's internal kinematics, and/or additional information on the resident MSP population will yield much stronger constraints and shed light about the origin of this otherwise mysterious γ-ray source.