In this paper, we investigate high frequency (HF) skywave massive multiple-input multiple-output (MIMO) communications with orthogonal frequency division multiplexing (OFDM) modulation. Based on the triple-beam (TB) based channel model and the channel sparsity in the TB domain, we propose a beam structured channel estimation (BSCE) approach. Specifically, we show that the space-frequency-time (SFT) domain estimator design for each TB domain channel element can be transformed into that of a low-dimensional TB domain estimator and the resulting SFT domain estimator is beam structured. We also present a method to select the TBs used for BSCE. Then we generalize the proposed BSCE by introducing window functions and a turbo principle to achieve a superior trade-off between complexity and performance. Furthermore, we present a low-complexity design and implementation of BSCE by exploiting the characteristics of the TB matrix. Simulation results validate the proposed theory and methods.