The Cotton-Mouton (Voigt) and Faraday effects induce adjustable linear and circular birefringence in optical media with external magnetic fields. We consider these effects as a technique for magneto-optical control of the transmission of bimodal light beams through Kerr-nonlinear crystals. Numerical analysis suggests that a properly applied magnetic field may accelerate, delay, or arrest the collapse of (2+1)D beams. Experimentally, the magnetic collapse acceleration is demonstrated in a bulk yttrium iron garnet (YIG) crystal.