This paper study the effect of interference management arising due to millimeter wave (mmWave) communication on the performance of multiple input multiple output (MIMO) based spectrum sharing cognitive systems. The highly directed mmWave signals have short wavelength property which enables to fabricate an increased number of antennas in a small confined space of the communication system. The large antenna elements are utilized to harvest high beamforming gains and to improve the signal to noise ratio (SNR) by analog processing at the cognitive base station (CBS) and secondary users. Analog processing at the CBS and at secondary user have hardware and computation restrictions. These restrictions are solved by designing radio frequency (RF) precoding and RF combining. In the digital domain, it is shown that interference between secondary users can be canceled by baseband block diagonalization technique. Towards this end, the underlay mode of operation is considered to control interference on the primary user and to derive the expression for optimal power allocation. The derived power allocation is a solution to the rate maximization problem of mmWave MIMO cognitive radio (CR) systems. Finally, numerical simulations are performed to yield various significant insights into for different mmWave CR system conditions and also validate the improvement in performance in comparison to the only digital communication systems.