The interaction forces between dust grains in a flowing plasma are strongly modified by the formation of ion wakes. Here, we study the interparticle forces mediated by ion wakes in the presence of a strong magnetic field parallel to the ion flow. For increasing magnetic flux densities a continuous decay of the interaction force is observed. This transition occurs at parameters, where the ion cyclotron frequency starts to exceed the ion plasma frequency, which is in agreement with theoretical predictions. The modification of the interparticle forces is important for the understanding of the structure and dynamics of magnetized dusty plasmas.