With the development of demands in various applications for array signal processing, the number of antennas in the array and the signal bandwidth are increasing. Several direction-of-arrival (DOA) estimation algorithms have been proposed for wideband signal sources. However, the wideband algorithms are generally more complex compared with the narrowband algorithms, especially in massive antenna array systems. In this paper, we focus on analyzing the bias of narrowband multiple signal classification (MUSIC) algorithm to obtain an effective bandwidth scope in the case of non-zero bandwidth signal sources, which can guide the selection of wideband and narrowband DOA estimation algorithm in real applications. To end it, we describe the time-domain array spatial covariance matrix in non-zero bandwidth case and analyze the trend of its eigenvalues with the signal fractional bandwidth. And then an approximation DOA estimation error expression of the MUSIC algorithm is derived based on Taylor series expansion of the null spatial spectrum function. The simulation results show that the narrowband MUSIC algorithm will appear to two extreme cases, which are approximately unbiased and completely invalid in massive antenna array systems.