This paper presents a multimode memory-based Fast Fourier Transform (FFT) processor for a medical system aimed at Fourier-domain optical coherence tomography (FD-OCT) capable of supporting wireless displays based on multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM). The proposed FFT processor enables the use of 2-stream 4096/2048/1024-point FFTs and 1- to 4-stream 128/64-point FFTs for FD-OCT and OFDM applications, respectively. Using cost-effective four-bank single-port SRAM operating in four-word data width, the proposed design provides data access for up to sixteen memory paths. In conjunction with a proposed FFT kernel devised using hardware-efficient multiplication and cache units, the proposed system allows high-throughput multimode FFT operations in an energy- and area-efficient configuration. A test chip was designed using TSMC-0.18 μm CMOS technology with a core size of 4.8 mm². Post-layout simulation performing 4096-point FFT at 80 MHz and the 128-point FFT at 40 MHz achieved throughput of 152 MS/s and 160 MS/s with power consumption of 156.2 mW and 69.9 mW, respectively. Compared to the previous approaches fully or partially supporting the specified OCT/OFDM FFTs, different degrees of area or energy efficiency improvements can be shown by our design depending on the FFT operation mode. In addition, system-level verification for practical OCT imaging was also performed using an FPGA platform.