Capillary instability and breakup of jets of magneto-rheological fluids are studied theoretically in the framework of one-dimensional theory. Linear instability is considered and the non-linear jet profile evolution is followed using numerical modelling. The magnetic field is assumed to be trapped within the liquid and both produces magnetic pressure and causes an increase in viscosity due to the magneto-rheological effect. Both effects of the magnetic field result in slowing down the necking and lead to development of a beads-on-string structure at the late stage of jet evolution. It is shown that the magneto-rheological effect by itself may prevent early breakup even in suspensions with strongly shear-thinning rheological behavior.