We demonstrate that light scattering by all-dielectric oligomers exhibits well-pronounced Fano resonances with strong suppression of the scattering cross section. Our analysis reveals that this type of the Fano resonance originates from the optically induced magnetic dipole modes of individual high-dielectric nanoparticles. By comparing to the plasmonic analogues, we observe that Fano resonances in all-dielectric oligomers are less sensitive to structural variations, which makes them promising for future applications in nanophotonics.