We used archival Hubble Space Telescope Wide Field Camera 3 (WFC3) images to obtain the luminosity function of the remote globular cluster NGC 2419 from 2 mag above the horizontal branch level down to ≃ 3.0 mag below the turn-off point (to MI≃ 6.4), approximately covering the range of initial stellar masses . The completeness-corrected luminosity function does not display any change of shape over the radial range covered by the WFC3 data, out to ≃ 6 core radii (rc), or, equivalently, to ≃ 2 half-light radii. The luminosity function in this radial range is also identical to that obtained from ground-based data at much larger distances from the cluster centre (), in the magnitude range in which the two distributions overlap (MI≤ 4.0). These results support the conclusion by Dalessandro et al. that there is no significant mass segregation among cluster stars; hence, the stellar mass-to-light ratio remains constant with distance from the cluster centre. We fitted the observed luminosity function with theoretical counterparts with the proper age and metallicity from different sets of stellar evolution models, and we consistently derive a total V-band mass-to-light ratio by extrapolating to the hydrogen-burning limit, with a best-fitting value M/LV= 1.5 ± 0.1. On the other hand, assuming that there are no cluster stars with m≤ 0.3 M⊙, we establish a robust lower limit M/LV > 0.8. These estimates provide useful constraints for dynamical models of the cluster that were forced to consider the stellar mass-to-light ratio as a (nearly) free parameter.