Pilot contamination incurred by strong inter-cell interference seriously degrades the performance of channel estimation in massive multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We propose an independent component analysis (ICA) and sparse recovery algorithm based semi-blind channel estimation scheme, referred to as sparse ICA (SICA), for multi-cell massive MIMO-OFDM systems, which does not require any prior information of intercell interference and therefore is more practical. The proposed SICA scheme enables accurate channel estimation by exploiting both the high-order statistics of the received signal and channel sparsity in angle domain. The SICA scheme performs in a semi-blind manner as it is much more robust against pilot overhead than the previous approaches, and requires only one OFDM symbol as pilot to achieve a superior normalized mean square error of channel estimation. Furthermore, the complexity required by SICA is much lower than that required by the previous work, thanks to the negligible complexity of interference sources number estimation based on sparse recovery algorithm.