In this Letter we report an observation of interference effects in Compton scattering in the experiment held on the VEPP-2000 collider. Infrared laser radiation was scattered head-on the 990 MeV electrons inside the dipole magnet, where an electron orbit radius is about 140 cm. It was observed that the energy spectrum of backscattered photons, measured by a HPGe detector, differs from that defined by the Klein-Nishina cross section and scattering kinematics of free electrons. The explanation of the effect, proposed in terms of classical electrodynamics, is in agreement with QED calculations.