Due to the massive data traffic in wireless networks, energy consumption has become a crucial concern, especially with the limited power supply of the mobile terminals and the increasing emission of the cellular industry. In this context, we study the energy efficiency (EE) of MIMO spectrum sharing cognitive radio (CR) systems under power and interference constraints. We present an energy-efficient power allocation framework based on maximizing the average EE per parallel channel resulting from the singular value decomposition (SVD) eigenmode transmission. We also present a sub-optimal low-complexity power allocation scheme based on the water-filling power allocation. In the numerical results, we show that the sub-optimal power allocation achieves at least of the optimal performance. In addition, we show that adopting more antennas is more energy efficient for a given power budget. Finally, we show that the interference threshold has a significant effect on both the EE and the spectral efficiency at high-power regime.