In this paper, we consider energy efficient transmissions for MIMO cognitive radio networks in which the secondary users coexist with the primary users. We want to optimize the proper time allocations and the beamforming vectors for the secondary users, in order to minimize the total energy consumption of the secondary users while satisfying secondary users' rate requirements and the primary receivers' received interference constraints. The joint time scheduling and beamforming optimization is non-convex and is often highly complex to solve. Fortunately, we show that the optimal time allocation and the optimal beamforming vectors can be found very efficiently in polynomial-time through a proper decomposition. The simulation results show that compared with a simplistic maximum rate transmission policy, our proposed energy-optimal-transmission algorithm can achieve an energy-saving of 26% to 91%, depending on the traffic load of the secondary system.