The production of ${\Sigma }^0$ baryons in the nuclear reaction p (3.5 GeV) + Nb (corresponding to $\sqrt{s_{NN}}=3.18$ GeV) is studied with the detector set-up HADES at GSI, Darmstadt. ${\Sigma }^0$s were identified via the decay ${\Sigma }^0\to \Lambda \gamma$ with subsequent decays $\Lambda \to p{\pi }^{-}$ in coincidence with a $e^{+}{e}^{-}$ pair from either external ($\gamma \to e^{+}{e}^{-}$) or internal (Dalitz decay ${\gamma }^{⁎}\to e^{+}{e}^{-}$) gamma conversions. The differential ${\Sigma }^0$ cross section integrated over the detector acceptance, i.e. the rapidity interval $0.5<y<1.1$, has been extracted as $\Delta {\sigma }_{{\Sigma }^0}=2.3\pm {\left(0.2\right)}^{stat}\pm {\left({}_{-0.6}^{+0.6}\right)}^{sys}\pm {\left(0.2\right)}^{norm}$ mb, yielding the inclusive production cross section in full phase space ${\sigma }_{{\Sigma }^0}^{total}=5.8\pm {\left(0.5\right)}^{stat}\pm {\left({}_{-1.4}^{+1.4}\right)}^{sys}\pm {\left(0.6\right)}^{norm}\pm {\left(1.7\right)}^{extrapol}$ mb by averaging over different extrapolation methods. The ${\Lambda }_{all}\text{/}{\Sigma }^0$ ratio within the HADES acceptance is equal to $2.3\pm {\left(0.2\right)}^{stat}\pm {\left({}_{-0.6}^{+0.6}\right)}^{sys}$. The obtained rapidity and momentum distributions are compared to transport model calculations. The ${\Sigma }^0$ yield agrees with the statistical model of particle production in nuclear reactions.