Based mainly on the distributed Bragg reflector (DBR) short linear cavity with a 1.6-cm-long heavily Tm3+-doped germanate glass fiber and semiconductor saturable absorber mirror (SESAM), a compact passively Q-switched single-frequency fiber laser at around 1950 nm is demonstrated experimentally. By comparing pulse characters of Q-switched operations fulfilled via SESAMs with different parameters, a stable output pulse is optimized to deliver a maximum average power of 22.2 mW, a peak power of 0.67 W, and an optical signal-to-noise ratio over 61 dB. Moreover, the repetition rate of the output pulse can be tuned from 92 to 520 kHz with a narrowest pulse width of 64 ns. To the best of our knowledge, this is the first time a 2.0 µm passively Q-switched single-frequency DBR Tm3+-doped fiber laser has been realized, and it shows great potential application in remote sensing, biomedical science, and nonlinear optics.