GaAs/InGaAs/GaAs nanowire core–multishell heterostructures with a strained radial In_0.2Ga_0.8As quantum well were fabricated by metal organic chemical vapor deposition. The quantum well exhibits a dislocation-free phase-pure zinc-blende structure. Low-temperature photoluminescence spectra of a single nanowire exhibit distinct resonant peaks in the range from 880 to 1000 nm, corresponding to the longitudinal modes of a Fabry–Pérot cavity. This suggests a decoupling of the gain medium and resonant cavity so that the quantum well provides the gain while the nanowire acts as the cavity. The resonant modes were observed at temperatures up to 240 K, exhibiting high power- and temperature-stability. The modes were blueshifted while decreasing the quantum well thickness due to enhanced quantum confinement. The results make the GaAs-based nanowire/quantum well hybrid structure promising for wavelength-tunable near-infrared nanolasers.