In the next generation of cellular communications, ultra-dense networking is a key to ensuring the coverage of millimeter-wave systems. On the other hand, hybrid precoding (HP) has been recognized as a promising technology for millimeter wave-based massive multiple-input multiple-output (MIMO) systems. However, few research efforts have been invested in handling multi-cell interference with hybrid precoding structure. In this paper, we propose a multi-cell interference processing scheme based on the ant colony system (ACS) method for massive MIMO interfering broadcast channels with hybrid precoding structure. Specifically, we first formulate the beam selection problem in the radio frequency (RF) domain as a traveling problem. Then with the goal of minimizing inter-cell signal-to-leakage-ratio (SLR), an ACS-based algorithm is proposed to provide the RF precoder design for each BS. Meanwhile, in each cell, the baseband combiner of each user is obtained by the singular value decomposition (SVD) method to maximize the corresponding channel gain, and the baseband precoder is provided by zero-forcing (ZF) algorithm to eliminate inter-user interference (IUI). Simulation results show that the proposed scheme can achieve effective beam selection to manage the multi-cell interference under massive MIMO broadcast channels, and the advantages of the proposed scheme in improving the sum rate for multi-cell systems compared with existing schemes.