FS Tau B is one of the few T Tauri stars that possess a jet and a counterjet as well as an optically visible cavity wall. We obtained images and spectra of its jet-cavity system in the near-infrared H and K bands using the Subaru/Infrared Camera and Spectrograph and detected the jet and the counterjet in the [Fe ii] 1.644 μm line for the first time. Within 2''the blueshifted jet is brighter, whereas beyond∼ 5''the redshifted counterjet dominates the [Fe ii] emission. The innermost blueshifted knot is spectrally resolved to have a large line width of∼ 110 km s− 1, while the innermost redshifted knot appears spectrally unresolved. The velocity ratio of the jet to the counterjet is∼ 1.34, which suggests that FS Tau B is driving an asymmetric jet, similar to those found in several T Tauri stars. Combining with optical observations in the literature, we showed that the blueshifted jet has a lower density and higher excitation than the redshifted counterjet. We suggest that the asymmetry in brightness and velocity is the manifestation of a bipolar outflow driving at different mass-loss rates, while maintaining balance of linear momentum. A full explanation of the asymmetry in the FS Tau B system awaits detail modeling and further investigation of the kinematic structure of the wind-associated cavity walls.