In this paper, we develop a new low-complexity linear frequency domain equalization (FDE) approach for continuous phase modulated (CPM) signals. As a CPM signal is highly correlated, calculating a linear minimum mean square error (MMSE) channel equalizer requires the inversion of a nondiagonal matrix, even in the frequency domain. In order to regain the FDE advantage of reduced computational complexity, we show that this matrix can be approximated by a block-diagonal matrix without performance loss. Moreover, our MMSE equalizer can be simplified to a low-complexity zero-forcing equalizer. The proposed techniques can be applied to any CPM scheme. To support this theory we present a new polyphase matrix model, valid for any block-based CPM system. Simulation results in a 60 GHz environment show that our reduced-complexity MMSE equalizer significantly outperforms the state of the art linear MMSE receiver for large modulation indices, while it performs only slightly worse for small ones.