This letter presents the optimal Bartlett detector based sequential probability ratio test (SPRT) for spectrum sensing in multi-antenna array cognitive radio networks. The optimal Wald test based sequential Bartlett spectral detector (S-BSD) is derived for a single/multiple primary user scenario, considering a fading wireless channel. Further, this is also extended to a scenario with multiple-input multiple-output (MIMO) wireless systems. Closed form expressions are derived for the average number of blocks required for the sequential detector in terms of the desired probability of false alarm and mis-detection. The S-BSD framework is also subsequently extended to an AWGN channel scenario. Simulation results are presented to illustrate the performance of the proposed detection schemes and verify the derived analytical results. The proposed S-BSD scheme is seen to significantly reduce the average number of symbols/blocks required to achieve the desired detection performance in comparison to the fixed block size BSD (F-BSD).