We report on a novel, noninvasive method applying Thomson scattering to measure the evolution of the electron beam energy inside a laser-plasma accelerator with high spatial resolution. The determination of the local electron energy enabled the in-situ detection of the acting acceleration fields without altering the final beam state. In this Letter we demonstrate that the accelerating fields evolve from (265±119) GV/m to (9±4) GV/m in a plasma density ramp. The presented data show excellent agreement with particle-in-cell simulations. This method provides new possibilities for detecting the dynamics of plasma-based accelerators and their optimization.