We experimentally demonstrate a stabilized single-frequency Brillouin fiber laser operating at 1.06 µm by means of a passive highly nonlinear fiber (HNLF) ring cavity combined with a phase-locking loop scheme. The stimulated Brillouin scattering efficiency is first investigated in distinct single-mode germanosilicate core fibers with increasing G e O 2 content. The most suitable fiber, namely, 21 mol.% G e O 2 core fiber, is used as the Brillouin gain medium in the laser cavity made with a 15-m-long segment. A Stokes lasing threshold of 140 mW is reported. We also show significant linewidth narrowing (below 1 kHz) as well as frequency noise reduction compared to that of the initial pump in our mode-hop free Brillouin fiber laser.