We present a butt-coupled InGaN fiber Bragg grating (FBG) semiconductor laser diode operating below 400 nm in the single-mode emission regime. This compact coherent laser source exhibits an intrinsic linewidth of 14 kHz in the near-UV range and a side-mode suppression ratio reaching up to 40 dB accompanied by almost 2 mW output power. Furthermore, the properties of the FBG, including its central wavelength, bandwidth, and reflectivity, can be readily customized to fulfill specific requirements. As a result, the small footprint design of this laser is compatible with integration into a standard butterfly package to ease the lab-to-market technology transfer. The combination of low-frequency noise and fibered output signal positions these FBG laser systems as strong candidates for hybridization with integrated photonic platforms tailored for quantum information processing and metrology.