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We use neutron powder diffraction to investigate the magnetic and crystalline structure of Cr$_2$GaN. A magnetic phase transition is identified at $T \approx 170$ K, whereas no trace of structural transition is observed down to 6 K. Combining Rietveld refinement with irreducible representations, the spin configuration of Cr ions in Cr$_2$GaN is depicted as an incommensurate sinusoidal modulated structure characterized by a propagating vector ${k}$=(0.365, 0.365, 0). Upon warming up to the paramagnetic state, the magnetic order parameter closely resembles to the temperature dependence of $c$-axis lattice parameter, suggesting strong magneto-elastic coupling in this compound. Therefore, Cr$_2$GaN provides a potential platform for the exploration of magnetically tuned properties such as magnetoelectric, magnetostrictive and magnetocaloric effects, as well as their applications.