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The magnetic, thermal and transport properties as well as electronic band structure of MnPtSi are reported. MnPtSi is a metal that undergoes a ferromagnetic transition at $T_{\mathrm{C}}=340$(1) K and a spin-reorientation transition at $T_{\mathrm{N}}=326$(1) K to an antiferromagnetic phase. First-principles electronic structure calculations indicate a not-fully polarized spin state of Mn in a $d^5$ electron configuration with $J=S=3$/2, in agreement with the saturation magnetization of 3~$\mu_{\mathrm{B}}$ in the ordered state and the observed paramagnetic effective moment. A sizeable anomalous Hall effect in the antiferromagnetic phase alongside the computational study suggests that the antiferromagnetic structure is non-collinear. Based on thermodynamic and resistivity data we construct a magnetic phase diagram. Magnetization curves $M$($H$) at low temperatures reveal a metamagnetic transition of spin-flop type. The spin-flopped phase terminates at a critical point with $T_{\mathrm{cr}}\approx 300$ K and $H_{\mathrm{cr}}\approx 10$ kOe, near which a peak of the magnetocaloric entropy change is observed. Using Arrott plot analysis and magnetoresistivity data we argue that the metamagnetic transition is of a first-order type, whereas the strong field dependence of $T_{\mathrm{N}}$ and the linear relationship of the $T_{\mathrm{N}}$ with $M^2$ hint at its magnetoelastic nature.