A novel type of a plasmonic sensor based on a magnetophotonic plasmonic heterostructure with an ultrahigh-Q resonance is considered. A magnetoplasmonic resonance with an angular width of 0.06A degrees, which corresponds to a Q factor of 700 and is a record value for magnetoplasmonic sensors, is experimentally demonstrated. It is shown that, owing to the excitation of long-propagation-range plasmons, the transverse magneto-optical Kerr effect is considerably enhanced and, thus, the sensitivity of the magnetoplasmonic sensor to variations in the refractive index increases to 18 RIU-1, where RIU is the refractive index unit. Numerical calculations indicate that the parameters of the magnetoplasmonic structure can be further optimized to attain sensitivities up to 5 x 10(3) RIU-1.