This Letter presents the first demonstration, to our knowledge, of a Brillouin optical time domain analysis (BOTDA) system based on a self-sweeping fiber laser. The unique feature of such laser sources is the generation of a narrowband tunable radiation with a small (6 MHz) tuning step and a reasonably large tuning range (3 GHz) making self-sweeping lasers extremely attractive for use in BOTDA systems. Since the wavelength tuning occurs solely due to internal processes occurring in the laser cavity, there is no need to use complex current/temperature control and feedback systems. This makes it possible to completely eliminate microwave devices, such as electro-optic modulators, from the BOTDA design. In this work, distributed temperature measurements with sensing line length of 25 km, spatial resolution of 10 m, and sensitivity of 2°C is demonstrated in a BOTDA system based on an Er-doped self-sweeping laser. The described approaches can reduce the complexity and overall cost of the BOTDA systems.