A method is proposed for the voltammetric determination of measles antibodies using a glassy carbon electrode modified with 2-propargylthio-6-nitro-7-hydroxy-4H-1,2,4-triazolo-4,7-dihydro[5,1-c]-1,2,4-triazine. An analytical signal was generated using a synthesized original compound attached to the surface of carboxylated carbon nanotubes through a thioline reaction and acted as a cross-linker for the immobilization of a bioreceptor, the measles virus antigen. We selected optimal working conditions for determining measles antibodies: signal recording mode, incubation time, temperature, pH of measurements, and concentration of the immobilized antigen. A calibration dependence I* (%) = –(1.5 ± 0.7)log с(IU/mL) + (29 ± 2) (R2 = 0.9653) was linear in the concentration range of measles antibodies 0.1–5.0 IU/mL. The limit of detection equal to 0.17 IU/mL, calculated using the 3σ test, ensures the use of the proposed method for the rapid analysis of biological fluids.