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Abstract Pattern formation and self-organization in many biological and non-biological systems can be explained through Turing’s activator-inhibitor model. Here we show how this model can be employed to describe the formation of filamentary structures in a low-pressure electric discharge exposed to a strong magnetic field. Theoretical investigation reveals that the fluid equations describing a magnetized plasma can be rearranged to take the mathematical form of Turing’s activator-inhibitor model. Numerical simulations based on the equations derived from this approach could reproduce the various patterns observed in the experiments. Also, it is shown that a density imbalance between electrons and ions exists in the bulk of the magnetized plasma that generates an electric field structure transverse to the applied magnetic field. This electric field is responsible for the stability of the filamentary patterns in the magnetized plasma over time scales much longer than the characteristic time scales of the electric discharge.