Using molecular dynamics simulations, we show that a simple model of a glassy material exhibits the shear localization phenomenon observed in many complex fluids. At low shear rates, the system separates into a fluidized shear band and an unsheared part. The two bands are characterized by a very different dynamics probed by a local intermediate scattering function. Furthermore, a stick-slip motion is observed at very small shear rates. Our results, which open the possibility of exploring complex rheological behavior using simulations, are compared to recent experiments on various soft glasses.