High-speed metal-semiconductor-metal (MSM) photodetectors based on Schottky-contacted core/shell GaAs/AlGaAs and bare GaAs nanowires were fabricated and characterized. The measured core/shell temporal response has a ∼10 ps full-width at half-maximum and an estimated corrected value less than 5 ps. The bare GaAs devices exhibit a slower response (∼35 ps) along with a slow decaying persistent photocurrent (∼80 s). The core/shell devices exhibit significantly improved dc and high-speed performance over bare nanowires and comparable performance to planar MSM photodetectors. The picosecond temporal response, coupled with picoampere dark current, demonstrate the potential for core/shell nanowires in high-speed imaging arrays and on-chip optical interconnects.