The finite amplitude nonlinear evolution of magnetic electron drift wave (MEDW) in collisionless electron magnetohydrodynamic plasmas is investigated. The dynamics of the nonlinear MEDW is shown to be governed by a Korteweg–de Vries–Zakharov–Kuztensov (KdV–ZK) equation in two dimensions which exhibits a soliton solution. The multi-dimensional stability using the small -k expansion yields that the magnetic electron drift solitary waves are unstable with respect to the perturbation in the transverse direction.