Beamforming plays an important role in 5G Massive Multiple-Input Multiple-Output (MMIMO) communications. Optimizing beamforming configurations for 5G base stations (BSs) can substantially improve the quality of service for mobile users, and thus has great practical value. However, identifying the optimal beamforming configurations has proven to be a complex task, and is even more challenging when accounting for the unavoidable coupled influence among multiple densely deployed 5G BSs. In this paper, we propose a highly efficient deep multi-agent Bayesian optimization framework for the coordinated beamforming optimization problem that involves multiple BSs. Its core algorithm is built upon a deep ensemble of neural networks and a sample-efficient upper confidence bound (UCB) based exploration strategy. Our numerical results show that the proposed approach is highly effective in searching for optimally coordinated beamforming vectors under extremely large search space, and beats strong multi-agent reinforcement learning baselines in terms of optimization quality and sample efficiency.