The present work is dedicated to characterization of the structural phase transition and incommensurate magnetic structure of the [CH3NH3][Ni(COOH)3] (1) perovskite-like metal-organic compound. The structural and magnetic characterization has been performed through variable-temperature single-crystal and powder neutron diffraction. Compound 1 crystallizes in the orthorhombic Pnma space group at room temperature. Below 84 K, a new phase has been observed. The occurrence of new reflections, which can be indexed with a wavevector along the c axis [q = 0.1426(2)c*], suggests the occurrence of an incommensurately modulated crystal structure. The structure was determined using the superspace group formalism on the Pnma(00γ)0s0 space group. This incommensurate phase remains unchanged with a decrease of the temperature up to the base temperature (ca. 2 K). Moreover, the magnetic susceptibility data, collected under zero-field-cooled and field-cooled conditions at different applied magnetic fields, show that compound 1 exhibits antiferromagnetic behavior below 34 K. In the current paper, we have confirmed that compound 1 presents the coexistence of nuclear and proper magnetic incommensurability below TN.