In this paper, we establish a general framework on the reduced dimensional channel state information (CSI) estimation and pre-beamformer design for frequency-selective massive multiple-input multiple-output (MIMO) systems employing single-carrier (SC) modulation in time division duplex (TDD) mode by exploiting the joint angle-delay domain channel sparsity in millimeter (mm) wave frequencies. First, based on a generic subspace projection taking the joint angle-delay power profile and user-grouping into account, the reduced-rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived for spatially correlated wideband MIMO channels. Second, the statistical pre-beamformer design is considered for frequency-selective SC massive MIMO channels. We examine the dimension reduction problem and subspace (beamspace) construction on which the RR-MMSE estimation can be realized as accurately as possible. It is observed that the proposed techniques show remarkable robustness to the pilot interference (or contamination) with a significant reduction in pilot overhead.