We report on the development of, to the best of our knowledge, the first ultrafast burst-mode laser system operating at a central wavelength of approximately 2 μm, where water absorption and, consequently, the absorption of most biological tissue is very high. The laser comprises a harmonically mode-locked 1-GHz oscillator, which, in turn, seeds a fiber amplifier chain. The amplifier produces 500 ns long bursts containing 500 pulses with 1 GHz intra-burst and 50 kHz inter-burst repetition rates, respectively, at an average power of 1 W, corresponding to 40 nJ pulse and 20 μJ burst energies, respectively. The entire system is built in an all-fiber architecture and implements dispersion management such that output pulses are delivered directly from a single-mode fiber with a duration of 340 fs without requiring any external compression. This gigahertz-repetition-rate system is intended for ablation-cooled laser material removal in the 2 μm wavelength region, which is interesting for laser surgery due to the exceptionally high tissue absorption at this wavelength.