We have measured the translational temperature dependence of the reaction rate constant for CH3CN + Ne+ → products at low temperatures. A cold Ne+ ensemble was embedded in Ca+ Coulomb crystals by a sympathetic laser cooling technique, while cold acetonitrile (CH3CN) molecules were produced by two types of Stark velocity filters to widely change the translational temperatures. The measured reaction rate constant gradually increases with the decrease in the translational temperature of the velocity-selected CH3CN molecules from 60 K down to 2 K, and thereby, a steep increase was observed at temperatures lower than 5 K. A comparison between experimental rate constants and the ion-dipole capture rate constants by the Perturbed Rotational State (PRS) theory was performed. The PRS capture rate constant reproduces well the reaction rate constant at a few kelvin but not for temperatures higher than 5 K. The result indicates that the reaction probability is small compared to typical ion-polar molecule reactions at temperatures above 5 K.