We realize a fiber Bragg grating InGaN-based laser diode emitting at 400 nm and demonstrate its high coherency. Thanks to the fabrication of a narrowband fiber Bragg grating in the near-UV, we can reach single-mode and single-frequency regimes for the self-injection locked diode. The device exhibits 44 dB side-mode suppression ratio and mW output power. Detailed frequency noise analysis reveals sub-MHz integrated linewidth and 16 kHz intrinsic linewidth. Such a narrow linewidth laser diode in the near-UV domain with a compact and low-cost design could find applications whenever coherency and interferometric resolutions are needed.