We address the problem of channel estimation in massive multiple-input multiple-output (Massive MIMO) systems where both hybrid analog-digital processing and low-resolution analog-to-digital converters (ADCs) are utilized. The hardware-efficient architecture is attractive from a power and cost point of view, but poses two significant channel estimation challenges. One is due to the smaller dimension of the measurement signal obtained from the limited number of radio frequency chains, and the other is the coarser measurements from the low-resolution ADCs. We address this problem by utilizing two sources of information. First, by exploiting the sparse nature of the channel in the angular domain, the channel estimate is enhanced and the required number of pilots is reduced. Second, by utilizing the transmitted data symbols as the “virtual pilots,” the channel estimate is further improved without adding more pilot symbols. The constraints imposed by the architecture, the sparsity of the channel and the data aided channel estimation are treated in a unified manner by employing a Bayesian formulation. The quantized sparse channel estimation is formulated into a sparse Bayesian learning framework, and solved using the variational Bayesian method. Simulation results show that the proposed algorithm can efficiently estimate the channel even with the architectural constraints, and that significant improvements are enabled by leveraging the transmitted data symbols.