Ce$_{2}$PtIn$_{8}$ is a recently discovered heavy-fermion system structurally related to the well-studied superconductor CeCoIn$_{5}$. Here, we report on low-temperature de Haas-van Alphen-effect measurements in high magnetic fields in Ce$_{2}$PtIn$_{8}$ and Pr$_{2}$PtIn$_{8}$. In addition, we performed band-structure calculations for localized and itinerant Ce-$4f$ electrons in Ce$_{2}$PtIn$_{8}$. Comparison with the experimental data of Ce$_{2}$PtIn$_{8}$ and of the $4f$-localized Pr$_{2}$PtIn$_{8}$ suggests the itinerant character of the Ce-$4f$ electrons. This conclusion is further supported by the observation of effective masses in Ce$_{2}$PtIn$_{8}$, which are strongly enhanced with up to 26 bare electron masses.