In this paper, we investigate the use of cyclic frequency diversity (CFD) scheme for single-carrier packet retransmission over frequency-selective channels in the context hybrid automatic repeat request protocols (HARQ). For each retransmission of the same packet, the transmitted signal is cyclically shifted in the frequency-domain in order to compensate for channel fading over a part of the channel bandwidth in the previous transmissions. We consider efficient frequency-domain equalization based on the minimum mean square error (MMSE) criterion. We determine an optimal solution for frequency-shift values in order to maximize system throughput by maximizing the signal to interference-plus-noise ratio (SINR) at the output of the joint MMSE equalizer. The CFD scheme has low complexity and provides a substantial gain in terms of frame error rate, especially for high rate channel coding.