Partially reduced graphene oxide (prGO) obtained by hydrothermal reduction was studied by electron paramagnetic resonance (EPR) spectroscopy in the temperature range 4.2–300 K. The EPR absorption is accompanied by nonresonant microwave absorption due to dielectric and conduction losses in prGO. This additional absorption is taken into account to determine correctly intensities of EPR spectra. The EPR spectra of prGO consist of the broad and narrow components. Above 100 K, the intensity of the broad component exhibits the Curie-Weiss behavior, but below 100 K it follows the Curie law revealing the disappearance of antiferromagnetic correlations. For the first time, the unusually strong increase of the narrow EPR signal intensity with lowering temperature is observed. This effect is explained by the Anderson localization of conduction electrons in the defected crystalline structure of prGO. Due to low spin density, the localized electrons become isolated and their magnetic susceptibility follows the Curie law with the temperature-dependent number of magnetic moments. Effects of adsorption of atmospheric gases on the observed properties are analyzed.