Optimal cooperative jamming (CJ) is studied for multiuser multiple-input multiple-output (MU-MIMO) broadcast channel to enhance the physical layer security with the help of a friendly jammer (FJ). We first derive a necessary and sufficient condition to achieve the asymptotically perfect security and propose an optimal CJ scheme to minimize the maximum signal-to-interference- plus-noise ratio (SINR) at the eavesdropper subject to a power constraint at the FJ. Then we derive an achievable lower bound of the eavesdropper's SINR and propose an asymptotically optimal CJ scheme achieving the lower bound. Numerical results demonstrate that the proposed schemes are effective.