Determination of the expression level of tumor marker PRAME protein is important both for predicting the course of the disease and for monitoring the effectiveness of anticancer therapy. A fluorescently labeled monoclonal antibody to the PRAME protein was obtained by periodate oxidation of glycans followed by modification with a bifunctional azido-oxyamine reagent and a “click” reaction with alkyne-modified sulfonated cyanine dye Cy3. A new approach to the synthesis of a bifunctional azido-oxyamine reagent using the ethoxyethylidene protecting group for oxyamine is proposed. The labeled antibodies were characterized with UV/Vis absorption spectra and the stoichiometry of the modification was determined. It has been demonstrated that the fluorescent antibodies retain affinity and can be used as a diagnostic tool for detecting the residual marker (the PRAME protein) after anticancer therapy.