Spurious electron self-interaction in density functional approximations (DFAs) can lead to inaccurate predictions of charge transfer in heteronuclear molecules that manifest as errors in calculated electrostatic dipoles. Here, we show the magnitude of these errors on dipoles computed for a diverse set of 47 molecules taken from the recent benchmark study of Hait and Head-Gordon [J. Chem. Theory Comput. 14, 1969 (2018)]. We compare the results of Perdew-Wang local spin density approximation (PW92), Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and strongly constrained and appropriately normed (SCAN) meta-GGA dipole calculations, along with those of their respective self-interaction-corrected (SIC) counterparts, to reference values from accurate wave function-based methods. The SIC calculations were carried out using the Fermi-Löwdin orbital (FLO-SIC) approach. We find that correcting for self-interaction generally increases the degree of charge transfer, thereby increasing the size of calculated dipole moments. The FLO-SIC-PW92 and FLO-SIC-PBE dipoles are in better agreement with reference values than their uncorrected DFA counterparts, particularly for strongly ionic molecules where significant improvement is seen. Applying FLO-SIC to SCAN does not improve dipole values overall. We also show that removing self-interaction improves the description of the dipole for stretched-bond geometries and recovers the physically correct separated atom limit of zero dipole. Finally, we find that the best agreement between the FLO-SIC-DFA and reference dipoles occurs when the molecular geometries are optimized using the FLO-SIC-DFA.