We present time-resolved spectral analysis of prompt emission from GRB 160625B, one of the brightest bursts ever detected by Fermi in its nine years of operations. Standard empirical functions fail to provide an acceptable fit to the GBM spectral data, which instead require the addition of a low-energy break to the fitting function. We introduce a new fitting function, called 2SBPL, consisting of three smoothly connected power laws. Fitting this model to the data, the goodness of the fits significantly improves and the spectral parameters are well constrained. We also test a spectral model that combines non-thermal and thermal (black body) components, but find that the 2SBPL model is systematically favoured. The spectral evolution shows that the spectral break is located around E_break ~100 keV, while the usual νF_ν peak energy feature E_peak evolves in the 0.5–6 MeV energy range. The slopes below and above E_break are consistent with the values –0.67 and –1.5, respectively, expected from synchrotron emission produced by a relativistic electron population with a low-energy cut-off. If E_break is interpreted as the synchrotron cooling frequency, the implied magnetic field in the emitting region is ~10 Gauss, i.e. orders of magnitudes smaller than the value expected for a dissipation region located at ~10¹³⁻¹⁴ cm from the central engine. The low ratio between E_peak and E_break implies that the radiative cooling is incomplete, contrary to what is expected in strongly magnetized and compact emitting regions.