Dynamically Programmable Gate Arrays (DPGAs) provide more area-efficient implementations than conventional Field Programmable Gate Arrays (FPGAs). One of typical DPGA architectures is multi-context architecture. An DPGA based on multi-context architecture is Multi-Context FPGA (MC-FPGA) which achieves fast switching between contexts. The problem of the conventional SRAM-based MC-FPGA is its large area and standby power dissipation because of the large number of configuration memory bits. Moreover, since SRAM is volatile, the SRAM-based multi-context FPGA is difficult to implement power-gating for standby power reduction. This paper presents an area-efficient and nonvolatile multi-context switch block architecture for MC-FPGAs based on a ferroelectric-capacitor functional pass-gate which merges a multiple-valued threshold function and a nonvolatile multiple-valued storage. The test chip for four contexts is fabricated in a 0.35µm-CMOS/0.60µm-ferroelectric-capacitor process. The transistor count of the proposed multi-context switch block is reduced to 63% in comparison with that of the SRAM-based one.