The CONNIE experiment is located at a distance of 30 m from the core of a commercial nuclear reactor, and has collected a 3.7 kg-day exposure using a CCD detector array sensitive to an ∼1 keV threshold for the study of coherent neutrino-nucleus elastic scattering. Here we demonstrate the potential of this low-energy neutrino experiment as a probe for physics Beyond the Standard Model, by using the recently published results to constrain two simplified extensions of the Standard Model with light mediators. We compare the new limits with those obtained for the same models using neutrinos from the Spallation Neutron Source. Our new constraints represent the best limits for these simplified models among the experiments searching for CEνNS for a light vector mediator with mass M Z < 10 MeV, and for a light scalar mediator with mass M φ < 30 MeV. These results constitute the first use of the CONNIE data as a probe for physics Beyond the Standard Model.