The zero-point quantum fluctuations of the electromagnetic field in vacuum are known to give rise to a long-range attractive force between metal plates (Casimir effect). For ferromagnetic layers separated by vacuum, it is shown that the interplay of the Casimir effect and of the magneto-optical Kerr effect gives rise to a long-range magnetic interaction. The Casimir magnetic force is found to decay as D⁻¹ in the limit of short distances, and as D⁻⁵ in the limit of long distances. Explicit expressions for realistic systems are given in the large- and small-distance limits. An experimental test of the Casimir magnetic interaction is proposed.