In this paper, we develop linear precoding methods for cognitive radio (CR) multi-user multiple-input multiple-output (MU-MIMO) broadcast systems where unlicensed secondary users (SUs) simultaneously use the same spectrum of the licensed primary user (PU). When the zero-forcing block diagonalization (ZF-BD) precoder is extended to the CR network, a noise enhancement problem occurs. Therefore, we propose a regularized BD precoder based on the minimum mean-square error (MMSE) criteria subject to zero interference constraint for the PU. As a result, the proposed MMSE-BD scheme improves the signal-to-interference-plus- noise ratio at each SU's receiver compared to the ZF-BD based method. Simulation results demonstrate that the proposed algorithm outperforms the ZF based technique by more than 5 dB at the sum-rate 10 bps/Hz for CR MU-MIMO downlink systems.