Diamond nanoparticles are promising photoluminescent probes for tracking intracellular processes, due to embedded, perfectly photostable color centers. In this work, the spontaneous internalization of such nanoparticles (diameter 25 nm) in HeLa cancer cells is investigated by confocal microscopy and time-resolved techniques. Nanoparticles are observed inside the cell cytoplasm at the single-particle and single-color-center level, assessed by time-correlation intensity measurements. Improvement of the nanoparticle signal-to-noise ratio inside the cell is achieved using a pulsed-excitation laser and time-resolved detection taking advantage of the long radiative lifetime of the color-center excited state as compared to cell autofluorescence. The internalization pathways are also investigated, with endosomal marking and colocalization analyses. The low colocalization ratio observed proves that nanodiamonds are not trapped in endosomes, a promising result in prospect of drug delivery by these nanoparticles. Low cytotoxicity of these nanoparticles in this cell line is also shown.