The production of Σ 0 baryons in the nuclear reaction p (3.5 GeV) + Nb (corresponding to √ s N N = 3.18 GeV) is studied with the detector set-up HADES at GSI, Darmstadt. Σ 0 s were identified via the decay Σ 0 → Λγ with subsequent decays Λ → pπ − in coincidence with a e + e − pair from either external (γ → e + e − ) or internal (Dalitz decay γ * → e + e − ) gamma conversions. The differential Σ 0 cross section integrated over the detector acceptance, i.e. the rapidity interval 0.5 < y < 1.1, has been extracted as ∆σ Σ 0 = 2.3 ± (0.2) stat ± +0.6 −0.6 sys ± (0.2) norm mb, yielding the inclusive production cross section in full phase space σ total Σ 0 = 5.8 ± (0.5) stat ± +1.4 −1.4 sys ± (0.6) norm ± (1.7) extrapol mb by averaging over different extrapolation methods. The Λ all /Σ 0 ratio within the HADES acceptance is equal to 2.3 ± (0.2) stat ± ( +0.6 −0.6 ) sys . The obtained rapidity and momentum distributions are compared to transport model calculations. The Σ 0 yield agrees with the statistical model of particle production in nuclear reactions.