Integrating radar and communication systems for economical use of hardware and spectrum resources is projected to be a crucial aspect of sixth-generation (6G) systems, leading to extensive research in the integrated sensing and communication (ISAC) area. In this article, we propose a radar detector structure for a multiple-input multiple-output (MIMO) ISAC system using orthogonal frequency-division multiplexing (OFDM) modulated waveforms. These waveforms are utilized to communicate with downlink (DL) users while receiving echoes from targets and clutter, in addition to separate OFDM-modulated uplink (UL) communication waveforms. The transmitter (Tx) and receiver (Rx) employ hybrid beamformers, with analog beamformers precisely designed to cover flat angular sectors. Tx and Rx beams are directed towards DL and UL users, respectively, with the possibility of overlapping or separate angular sectors. We introduce a Doppler-aware Code Bank (DACB) as the initial processing stage, thoroughly investigating the effects of Doppler mismatch. Following DACB, a sub-optimal sequential angle-range processing (SARP) method is proposed to maximize the output signal-to-interference-plus-noise ratio (SINR) while maintaining feasible processing. A two-variant detector scheme is proposed to address this processing’s suboptimality. Four different detectors with varying complexities, including a fully adaptive detector, are introduced. The potential beam-squint (BS) effect due to increased bandwidth is also considered, and a subband approach is proposed to mitigate these effects. Simulation results for all four detectors, as well as a conventional 3-dimensional periodogram detector commonly used as a benchmark in the literature, are provided. The results demonstrate that the proposed detectors can significantly enhance SINR and the probability of detection, particularly when accounting for the coupling between the clutter Doppler and Tx OFDM symbols.