Photoluminescence quenching of single dibenzoterrylene (DBT) dye molecules in a polymeric organic light-emitting diode was utilized to analyze the current dynamics at nanometer resolution. The quenching mechanism of single DBT molecules results from an increase in the triplet-state population induced by charge carrier recombination on individual guest molecules. As a consequence of the long triplet-state relaxation time, its population results in a reduced photoluminescence of the dispersed fluorescent dyes. From the decrease in photoluminescence together with photon correlation measurements, we could quantify the local current density and its time-dependent evolution in the vicinity of the single-molecule probe. This optical technique establishes a non-invasive approach to map the time-resolved current density in organic light-emitting diodes on the nanometer scale.