We present an all-fiber all-optical high-speed wavelength-swept laser source at 2 μm with a 3-dB bandwidth of 33 nm and repetition rate of 18.4 MHz, by using optical time-stretch technology, which to our knowledge is the first report of a 2 μm wavelength-swept source without any bulk, free-space optical elements. The light source is built upon a nonlinear polarization rotation mode-locked femtosecond oscillator. A chirped fiber Bragg grating (CFBG) is employed to realize the all-optical wavelength sweeping. In comparison with the commonly used dispersive fibers, the CFBG possesses outstanding power efficiency and temporal stability, especially for wavelength sweeping in the 2.0 μm wavelength regime. A two-stage fiber amplifier system is utilized to boost the output power up to 1.01 W. This all-fiberized mode-locked swept source with high speed and high stability shows great potential as a valuable source for various spectroscopy applications and swept source optical coherence tomography, particularly for highly scattering medium with low water content.