<p>We show that the electromagnetic proximity effect in superconductor (S) / ferromagnet (F) bilayers favors the formation of magnetic domains in the ferromagnet for the broad range of system parameters. Specifically, for the model of the isolated domain wall separating two domains we determine the energetically favorable domain thicknesses and the magnetic texture. Depending on the F layer thickness the magnetic moments in the neighboring domains are shown to be anti-parallel or noncollinear provided the ferromagnet has easy-plane magnetic anisotropy. Such instability of a homogeneous magnetic state is of particular importance in the design of the superconducting spintronics devices.</p>